Statements

A theorem, a lemma, a proposition, a corollary, a fact or an axiom.

Name	Tag	Kind	Level	MSC
The integers are a Euclidean domain	000JFQGDXG	statement	W0	11A05
Sequential characterization of limits heine-definition-of-limit	000MXHEY22	statement	W0	26A03
Singular value decomposition	000NPTMX6J	statement	W1	15A18, 15A23
Power series are differentiable inside the radius of convergence	002X7EK91H	statement	W0	30B10, 26A24
A function with zero derivative is constant	003QDZ4T16	statement	W0	26A24
Closure is the set of limits of sequences	003QP7A8HG	statement	W0	54E35
A differentiable function is convex iff its derivative is increasing	005JT76HCK	statement	W0	26A51
Taylor's theorem with the Cauchy remainder	005Q84BMAD	statement	W0	41A80
The characteristic of an integral domain is zero or prime	00758QM6JJ	statement	W0	13G05
Dimension of the dual space	00889YD15K	statement	W0	15A03, 15A04
Scaling a row scales the determinant	009CY8JXFX	statement	W0	15A15
Stars and bars	009TEMTQKH	statement	W0	05A10
Picard–Lindelöf theorem in integral form	00BT70ND50	statement	W0	34A12
Finite intersection property compactness-via-the-finite-intersection-property	00BWV5CKCF	statement	W0	54D30
Addition formula for Fibonacci numbers	00CN2F997Q	statement	W0	11B39
The logarithm grows slower than any power	00DGYY10FV	statement	W0	26A12, 33B10
Laws of exponents in a group power-laws-in-a-group	00DRK90Z6K	statement	W0	20A05
−1 is a square modulo p if and only if p is not 3 modulo 4	00DW862T78	statement	W0	11A15
Congruence is compatible with addition	00FWBN7F0Y	statement	W0	11A07
Intermediate value theorem bolzano-theorem	00KAFBR32E	statement	W1	26A15
Modulus of the conjugate	00KRCVE7CK	statement	W0	30A99
Every vector space has a basis	00MS9VMQ9Z	statement	W0	15A03, 03E25
Change of variables in multiple integrals substitution-rule-several-variables, jacobian-change-of-variables	00N5FHP1CV	statement	W0	26B15
Derivative of sine	00R4MWW532	statement	W0	33B10, 26A24
Divergence of the sum of the reciprocals of the primes	00RA98X2CP	statement	W0	11N05
Ramsey's theorem	00TQV3F5S4	statement	W1	05D10, 05C55
A finite group is nilpotent iff it is the product of its Sylow subgroups	00Y9N80VSS	statement	W0	20F18, 20D15
Volume of a ball in R^n volume-of-an-n-ball	00YH28R457	statement	W0	28A75
Additivity of line integrals under concatenation line-integral-over-a-sum-of-paths	00ZEBSMNNV	statement	W0	26B12
Uniqueness of finite fields of a given order	010PKCQPXP	statement	W0	12E20
Hensel's lemma	010QVB71T2	statement	W1	11A07
Recurrence for Bell numbers	0110GBHPPB	statement	W0	11B73
A convex function on an open interval is continuous	011HV2GAWF	statement	W0	26A51
Jordan–Chevalley decomposition	011K11VPJN	statement	W0	15A21, 15A20
1 + x is at most exp x	012C7GFF20	statement	W0	33B10, 26D15
exp z = 1 iff z is an integer multiple of 2πi kernel-of-the-exponential	013AHC4DRT	statement	W0	33B10
Existence of splitting fields	01441KDGBY	statement	W0	12F05
Chernoff bound	014PEBGDYF	statement	W0	60E15
Cayley's theorem	0151VYVX27	statement	W1	20B30
Integral equation form of an initial value problem	015KK993C5	statement	W0	34A12
Leibniz formula for determinants	016PE4VZ8Q	statement	W0	15A15
Riemann's criterion for integrability	017DH8WXTE	statement	W0	26A42
Dyck words are counted by Catalan numbers	017SRZ7NE9	statement	W0	05A15
Rolle's theorem	0194DY35BG	statement	W1	26A24
Residue at a simple pole residue-formula-for-simple-poles	01991NCP7H	statement	W0	30E20
Derivative of the complex exponential	019H1Z6419	statement	W0	33B10
Integral test integral-test-for-convergence	019QZ6RRVH	statement	W0	40A05
First derivative test	01A2EGXJEM	statement	W0	26A24
cos pi = -1	01A8JGR4JM	statement	W0	33B10
Distance from a point to a line	01AAYNSBN6	statement	W0	51N20
Chapman–Kolmogorov equation chapman-kolmogorov-equations	01APZ8GDQH	statement	W1	60J10
Well-ordering principle	01BX15HSRR	statement	W1	03F30
The complex numbers cannot be ordered	01CJRJKDAA	statement	W0	12J15
Normality via left and right cosets	01E7SWYJX3	statement	W0	20A05
Determinant of a scalar multiple	01EXSMK864	statement	W0	15A15
Extensions of solvable groups are solvable	01EY0EM7RP	statement	W0	20F16
Urysohn's lemma urysohn-lemma	01EY3VR7ZD	statement	W1	54D15
Composition of injections is injective injective-comp	01FPXMTBX1	statement	W0	03E20
Equivalence classes form a partition	01HT2CH8BH	statement	W0	03E20
Vandermonde's identity	01JADB9VW5	statement	W1	05A19
Triangle inequality for a metric triangle-inequality-for-a-metric	01M6CW9VM6	statement	W0	54E35
Cauchy's integral theorem cauchy-goursat-theorem, cauchy-integral-theorem	01MPZXYVYF	statement	W1	30E20
sin x / x tends to 1	01QSSKS5C1	statement	W0	33B10
Sum of the first n natural numbers	01QZNHQWYD	statement	W0	05A19
A graph is bipartite iff it has no odd cycle	01R1HPEK6S	statement	W0	05C75
Symmetry of second derivatives equality-of-mixed-partials	01V9FPBBVK	statement	W1	26B05
Bijective iff it has a two-sided inverse	01VG2A0BHW	statement	W0	03E20
Uniqueness of the algebraic closure	01VQ7C4FTB	statement	W0	12F05
Cantor set is closed	01VT24J1SD	statement	W0	54F65
Arguments add under multiplication	01W6RKJP01	statement	W0	30A99
Legendre's formula de-polignac-formula	01WPV9PHN7	statement	W0	11A51
Cassini's identity	01WQZK97Z5	statement	W0	11B39
Adding a multiple of one row to another preserves the determinant	01ZTQBK64Q	statement	W0	15A15
Law of the unconscious statistician lotus, change-of-variables-formula-for-expectation	01ZWX875AT	statement	W0	60A05
Carathéodory's theorem	0201Q4P2B5	statement	W1	52A35
Euler's theorem on Eulerian circuits	020422MDQF	statement	W0	05C45
Existence of prime factorization	020K0X7HVR	statement	W0	11A51
Darboux and Riemann integrals agree	021XJAQVDC	statement	W0	26A42
Uniqueness of solutions for Lipschitz vector fields	025PKW8AMR	statement	W0	34A12
A function with nonnegative derivative is increasing	026BJBQNGJ	statement	W0	26A24
Uniformly continuous functions map Cauchy sequences to Cauchy sequences	026FDZFRXS	statement	W0	26A15
Parallelogram law	026HPGYGS4	statement	W1	46C05
Quotients of solvable groups are solvable	027ZQS04SJ	statement	W0	20F16
Angle addition formulas	028XEQCE88	statement	W0	33B10
Euclid's theorem infinitude-of-primes	0292EPPPT0	statement	W1	11A41
Holomorphic functions on a disc have primitives existence-of-primitives-on-a-disc	02AC7JR6G6	statement	W0	30E20
Eisenstein's criterion	02BPKD7TMD	statement	W1	12E05
Mean value inequality	02CYB184RC	statement	W0	26B05
Open balls form a basis of the metric topology	02EEX96DFS	statement	W0	54E35
Rank of a product of matrices	02FDWY55AS	statement	W0	15A03
Casorati–Weierstrass theorem sokhotski-theorem, casorati-weierstrass-sokhotski-theorem	02HHNPC8ED	statement	W0	30D30
Existence of maximal ideals krull-s-theorem	02HJYT53F7	statement	W0	13A15
Chebyshev's inequality bienayme-chebyshev-inequality	02HZ1BK3MW	statement	W1	60E15
Isometries are injective	02J4G4J4TJ	statement	W0	54E40
Characteristic function of a sum of independent random variables	02JGYG0T7M	statement	W0	60E10
Power series of sine	02KTRHQMHN	statement	W0	33B10, 30B10
The complex exponential is 2πi-periodic periodicity-of-the-exponential	02P2PYH3X3	statement	W0	33B10
Sum of the roots of unity	02PETK9PQ4	statement	W0	11R18
Cauchy mean value theorem extended-mean-value-theorem	02SYZAWM2K	statement	W0	26A24
Closure is closed	02TZDKG50Q	statement	W0	54A05
Decreasing sequence bounded below converges	02V2GYAC8P	statement	W0	40A05
Riemann mapping theorem riemann-mapping	02WHMEG5ZR	statement	W1	30C35
K5 and K3,3 are not planar	030A3FHN14	statement	W0	05C10
The real part of a holomorphic function is harmonic	031BG625Y3	statement	W0	31A05
A tangent is perpendicular to the radius	031JV5S54D	statement	W0	51M04
Order of a cyclic subgroup equals the order of its generator	031M8HX7DA	statement	W0	20A05
Residue theorem cauchys-residue-theorem	032HKYS329	statement	W1	30E20
Factorial formula for binomial coefficients	033KTKKRV6	statement	W0	05A10
Formula for the modulus	034FGCEYX4	statement	W0	30A99
Triangularisation	0363JMQ42Y	statement	W0	15A20, 15A21
Gauss's lemma on quadratic residues gauss-lemma	037ACYXB5Z	statement	W0	11A15
Leibniz formula for pi madhava-leibniz-series	037FD5NBRT	statement	W1	40A05
Arzelà–Ascoli theorem ascoli-theorem	0381S8Z5P0	statement	W0	54C35
Freshman's dream	0396VGFA78	statement	W1	13A35
Taylor's theorem with the Peano remainder	03AJHX431A	statement	W0	41A58
Generalized Euclid's lemma	03BAREW1Z5	statement	W0	11A05
Law of total variance variance-decomposition-formula, eve-law	03BY5XTNA4	statement	W0	60A10
Variance of the normal distribution	03EESZDB9A	statement	W0	60E05
Vector triple product triple-product-expansion, bac-cab-identity	03FTB26QYD	statement	W0	15A72
Chain rule for Jacobian matrices	03GGQEAG9S	statement	W0	26B10
Pythagorean trigonometric identity	03H7WZ4T3K	statement	W0	33B10
Triangle inequality	03HF5PMY5T	statement	W1	26A03
Mean value theorem in several variables	03HGK7EW6R	statement	W0	26B05
Wilson's theorem	03KGGKTB2E	statement	W1	11A07
Equivalence of norms in finite dimension	03MC70ZRNR	statement	W0	46B20
de Moivre's formula	03MTBVG3VE	statement	W1	33B10
Vectors are perpendicular if and only if their dot product is zero	03NK6RSRQ1	statement	W0	51N20
Cauchy–Schwarz inequality for expectations cauchy-schwarz-inequality-for-random-variables	03PGHKAJG3	statement	W0	60E15
A matrix is invertible iff its determinant is a unit	03Q7RE2HXR	statement	W0	15A15
Complement principle	03QC59M99B	statement	W0	05A05
Taylor's theorem	03QHBVW4TT	statement	W1	41A58
Formula for the number of derangements	03RSJXF728	statement	W0	05A05
Limit of a quotient of sequences	03S6GWWKEZ	statement	W0	40A05
Sum of a finite geometric progression finite-geometric-series	03X8V7D64M	statement	W0	05A19
Open mapping theorem open-mapping-theorem-complex-analysis	03YEM7JEDN	statement	W0	30A99
C^1 vector fields satisfy the Picard–Lindelöf hypotheses	03Z9V0Y78A	statement	W0	34A12
Binet's formula	0404D8TN7Y	statement	W0	11B39
Lebesgue number lemma lebesgues-number-lemma	040CFNJEAP	statement	W0	54E45
Subgroups of a finite cyclic group correspond to divisors of its order fundamental-theorem-of-cyclic-groups	0423TXR9AN	statement	W0	20K01
Rational canonical form frobenius-normal-form	042JWAR3Q0	statement	W1	15A21
Continuous bijection from a compact space to a Hausdorff space is a homeomorphism	0430ETCMKD	statement	W0	54D30
Uniform limits of holomorphic functions are holomorphic weierstrass-convergence-theorem	0431RN0R1N	statement	W0	30A99
Fermat's theorem on sums of two squares fermat-christmas-theorem	043B3ENSTY	statement	W1	11E25
The derangement numbers count derangements	045ENVCCZV	statement	W0	05A05
Monotonicity of probability	0464Z0JP2E	statement	W0	60A05
Every real number has a decimal expansion	047KEVEZ9Q	statement	W0	11A63
Parseval's identity	047RFCNVSK	statement	W1	46C05
Maximum modulus principle maximum-modulus-theorem	048F2P90WR	statement	W1	30C80
Lagrange multiplier with one constraint lagrange-multiplier-single-constraint	04A2XEX4D4	statement	W0	90C46
Exponential of a sum of commuting matrices	04BD23PSK5	statement	W0	15A16
log x is at most x - 1	04CBRA4JRK	statement	W0	33B10, 26D15
Determinant is multiplicative	04CPJ6AF00	statement	W0	15A15
Spectral theorem for normal matrices	04CW1P44VD	statement	W0	15A21, 47B15
Variance under translation variance-is-shift-invariant	04CYN5G6RY	statement	W0	60A05
Order of a group is the index times the order of the subgroup	04DC0SRN2K	statement	W0	20D60
Uniqueness of the supremum	04ETX30HT2	statement	W0	06A06
Riesz representation theorem in finite dimensions	04GYPXDXNH	statement	W0	46C05, 15A04
Density of the irrationals	04J6G4H78J	statement	W0	26A03
Dirichlet's approximation theorem	04JAY9DGB7	statement	W0	11J04
Hockey-stick identity	04JHQNNBFE	statement	W1	05A19
Sum of two squares theorem	04NPWJMA6H	statement	W1	11E25
Euler's formula	04R3CY41VJ	statement	W1	33B10
Cyclic groups are abelian	04RG02S6BA	statement	W0	20A05
Law of total expectation tower-property, law-of-iterated-expectations, adam-law	04RRB6HM00	statement	W0	60A10
Zorn's lemma zorn-lemma, kuratowski-zorn-lemma	04RXTQA5ZA	statement	W1	03E25
Chinese remainder theorem for non-coprime moduli	04SJTX9P4N	statement	W0	11A07
Contrapositive contraposition, law-of-contraposition	04T1CT7212	statement	W0	03B05
Multiplicativity of the divisor function	04WC36XKV6	statement	W0	11A25
Integral of cosine	04WTBQ7APQ	statement	W0	26A36
Existence of primitive roots modulo a prime	04XGKK8WQW	statement	W0	11A07
Every connected graph has a spanning tree	04XPQT2XTC	statement	W0	05C05
Monotone functions are Riemann integrable	04YKAYDQPW	statement	W0	26A42
Comparison test direct-comparison-test	04Z5G0THN6	statement	W1	40A05
The real numbers are uncountable uncountability-of-the-reals	0518MM6BE1	statement	W0	03E10
Euclid's lemma	051VYKA1EX	statement	W1	11A05
Product of a matrix and its adjugate	0528HKWZ1Z	statement	W0	15A09, 15A15
Eigenvalues are the roots of the characteristic polynomial	053QVHF6N7	statement	W0	15A18
Compact iff complete and totally bounded	054Q5PW5GX	statement	W0	54E45
Fermat numbers are pairwise coprime goldbach-theorem-fermat-numbers	05598J0Y8R	statement	W0	11A41
PID implies UFD	055HT85T3S	statement	W0	13F15
Lebesgue's criterion for Riemann integrability lebesgue-vitali-theorem	0565EGK6XP	statement	W0	26A42
A matrix is diagonalisable iff it has a basis of eigenvectors	056SW1E0AC	statement	W0	15A20
Isosceles triangle theorem pons-asinorum, base-angles-theorem	056VS31A0J	statement	W0	51M04
Generating function for partitions	0578PA53VA	statement	W0	11P81
The nth roots of unity	057BH3JC9S	statement	W0	11R18
Number of compositions	057H72B2MB	statement	W0	05A17
Ptolemy's theorem	058YS05YP5	statement	W1	51M04
Scalar triple product mixed-product, box-product	059Q2XWJDC	statement	W0	15A72
Isomorphism with the coordinate space	059THXBRBB	statement	W0	15A03
Sum of a finite geometric series	05APWSX53S	statement	W0	40A05
Expectation of a product of independent random variables multiplicativity-of-expectation	05AW1G0WE1	statement	W0	60A05
Stabilisers of points in the same orbit are conjugate	05BM304NRX	statement	W0	20B05
Zeckendorf's theorem	05DEJR6TGF	statement	W1	11B39
Polarisation identity	05FKHRT0B4	statement	W1	46C05, 15A63
Root test cauchy-root-test	05H4DDDYBZ	statement	W1	40A05
Inner automorphism group is isomorphic to G modulo its centre	05HYGWFG63	statement	W0	20F28
Poincaré lemma for one-forms on convex sets poincare-lemma	05MC3HND79	statement	W0	58A12
Angle sum of a triangle triangle-angle-sum-theorem	05MDKQBEAF	statement	W0	51M04
Groups of prime order are cyclic	05MM4EK4SA	statement	W0	20D60
Subgroup criterion one-step-subgroup-test	05N4TQKPH0	statement	W0	20A05
Composition of continuous maps is continuous	05NK26G0DR	statement	W0	54C05
Derivative of arctangent	05P4B4Q22V	statement	W0	33B10, 26A24
Markov's inequality	05PWWHYBX5	statement	W1	60E15
Matrix of a composition is the product of matrices	05Q1B7MH0M	statement	W0	15A04
Additivity of the integral over intervals	05RCDKHZM6	statement	W0	26A42
Laplacian as a sum of second partial derivatives cartesian-formula-for-the-laplacian	05RCT1522R	statement	W0	35J05
Number of edges of a complete graph	05RN90E14Y	statement	W0	05C30
Harmonic numbers grow like log n	05S2GSPMGA	statement	W0	11B83, 26A12
Negation of an existential statement	05SZQKH75K	statement	W0	03B10
Equality of complex numbers	05V7J4WD1C	statement	W0	30A99
Maximal ideals are prime	05WAF5T0GZ	statement	W0	13A15
Jacobian of spherical coordinates spherical-volume-element	05WKRC7HWT	statement	W0	26B15
Subgroups of solvable groups are solvable	05Y0F9M0TS	statement	W0	20F16
Law of cosines cosine-rule	060ZVZBV3E	statement	W1	51M04
Lucas–Lehmer test lucas-lehmer-primality-test	061BTYA0RN	statement	W1	11Y11
First fundamental theorem of calculus	063H5KJC69	statement	W0	26A42
LaSalle's invariance principle invariance-principle, krasovskii-lasalle-principle	0659J5X7B5	statement	W0	34D20, 34D23
Inclusion of a subspace is continuous	065J822CKN	statement	W0	54B05
Repeating decimals are rational	065S5B9HF1	statement	W0	11A63
De Moivre–Laplace theorem de-moivre-laplace-theorem, normal-approximation-to-the-binomial	065X9S8CM3	statement	W1	60F05
Closed subsets of compact sets are compact	066HW6D9A7	statement	W0	54D30
The integers are countable	066RJJVWH9	statement	W0	03E10
Repeated roots and the derivative	067F8YVYMH	statement	W0	13F20
Tonelli's theorem tonelli-theorem	067SYD2J4B	statement	W0	28A35
Existence of square roots of nonnegative reals	068BZBXE0C	statement	W0	26A09
Closure in a metric space	068P0P32DW	statement	W0	54E35
Uniqueness of splitting fields	069A3BC3EP	statement	W0	12F05
Comparison of a series and an integral	069HKV4X1E	statement	W0	26A42
Laplace expansion along a column	06AMCJMMVM	statement	W0	15A15
Heine–Cantor theorem heine-cantor-theorem	06B8BNJCD6	statement	W0	54E45
Solution formula for linear first-order equations	06B9W45XV0	statement	W0	34A30
Five colour theorem	06C0JBE52D	statement	W0	05C15, 05C10
Integral of the exponential function	06D0EWR2DV	statement	W0	26A36
Dimension of a direct product	06HN47VPTH	statement	W0	15A03
Grassmann's formula dimension-formula	06HTJNCMPA	statement	W0	15A03
Spectral theorem	06J4PXRG22	statement	W1	47B15, 15A18
Classification of finite simple groups enormous-theorem	06J6P03MG7	statement	W1	20D05
Power series of the exponential function	06JZGMYTYD	statement	W0	33B10
The minimal polynomial divides every polynomial vanishing at the element	06K7SARZKR	statement	W0	12F05
Every spanning set contains a basis	06MRNP4BNT	statement	W0	15A03
Cauchy criterion for series	06PVXMY0TH	statement	W1	40A05
Dimension of the annihilator	06Q1EFVH0Q	statement	W0	15A03, 15A04
cosh^2 - sinh^2 = 1	06QCTRFBM0	statement	W0	33B10
Units of the Gaussian integers	06RH4XAGRY	statement	W0	11R11
Number of invertible residues modulo n	06RJWZCG95	statement	W0	11A07
Continuous functions are Riemann integrable	06SESV7GQY	statement	W0	26A42
Existence of Laurent expansions on an annulus laurents-theorem, laurent-expansion-theorem	06WHRARZKY	statement	W0	30B10
Converse of Wilson's theorem	06WRV8HFDY	statement	W0	11A51
Continuous image of a closed interval is a closed interval	06ZARTQTQE	statement	W0	26A15
Geometric formula for the dot product	070TXS9AXM	statement	W0	51N20
Congruence is compatible with multiplication	072D5G4SK6	statement	W0	11A07
Limit of a product of sequences	0734RSVF2V	statement	W0	40A05
Cyclic groups of the same order are isomorphic	0736AXH2ME	statement	W0	20A05
Third isomorphism theorem for rings	073C80EC63	statement	W0	16D25
Associativity of matrix multiplication	073E4XC016	statement	W0	15A99
Kolmogorov's zero–one law kolmogorov-0-1-law, kolmogorov-zero-one-law	073Q8Z94KG	statement	W0	60F20
Correspondence between equivalence relations and partitions fundamental-theorem-of-equivalence-relations	074482Q7CD	statement	W0	03E20
One-sided inverse of a square matrix is two-sided	0753Y2X5K6	statement	W0	15A09
The reals have the cardinality of the continuum cardinality-of-the-reals	075PM9FH7A	statement	W0	03E10
Uniqueness of the derivative	0762WAE49P	statement	W0	26B05
Independent random variables are uncorrelated	077GN9HDR6	statement	W0	60A05
Determinant of the inverse	0783S9D0ZH	statement	W0	15A15
Continuity of the inverse of a strictly monotone continuous function	07BY47HG5S	statement	W0	26A48
Classification of finite abelian groups fundamental-theorem-of-finite-abelian-groups, basis-theorem-for-finite-abelian-groups	07CQR9BW3R	statement	W0	20K01
Lcm of coprime integers	07CZYE06ZJ	statement	W0	11A05
Lipschitz maps are uniformly continuous	07DCKDXRBP	statement	W0	26A16
Cauchy–Hadamard theorem cauchy-hadamard-formula	07E5MB1CA2	statement	W1	30B10
Disjoint cycles commute	07E6D8R4D6	statement	W0	20B30
Composition of surjections is surjective surjective-comp	07EH4R3RVQ	statement	W0	03E20
Grönwall's inequality gronwall-lemma, gronwall-bellman-inequality	07EJHQYR9A	statement	W0	26D10, 34A40
Pépin's test	07HXA8KV6F	statement	W1	11Y11
A function with positive derivative is strictly increasing	07J5X2T1ZX	statement	W0	26A24
i squared is minus one	07KBQCG9KV	statement	W0	12D99
If 2^p − 1 is prime then p is prime	07MMWAXMYD	statement	W0	11A41
Fermat's Last Theorem for n = 3	07NKG38VEG	statement	W0	11D25
Menelaus's theorem	07NSKDGS7S	statement	W1	51M04
Heine–Borel theorem heine-borel-theorem	07PFYV65MB	statement	W1	54E45
Möbius inversion formula	07Q4TBTFVB	statement	W1	11A25
Third isomorphism theorem for vector spaces	07RB3EMBWW	statement	W0	15A03, 16D10
Derivatives of the hyperbolic functions	07T2TKGZ4J	statement	W0	33B10, 26A24
Young's inequality for products	07VHQ31EYJ	statement	W1	26D15
Derivative of the logarithm	07X1QA6BRW	statement	W0	33B10, 26A24
Differentiable functions are continuous	07ZMX4ANJS	statement	W0	26A24
Anticommutativity of the cross product	07ZS685JJC	statement	W0	15A72
Every integer is a square times a square-free integer	080Q3RPKY6	statement	W0	11A51
Linearity of the integral	080RWVVSB6	statement	W0	26A42
Rational root theorem rational-root-test	0819CQ1V8H	statement	W1	12E05
Finite p-groups are nilpotent	081WTKYX6C	statement	W0	20D15, 20F18
Holomorphic functions are analytic analyticity-of-holomorphic-functions	0826SGV3R0	statement	W0	30B10
Absolutely convergent series in a Banach space converge	082MGNWNA8	statement	W0	40A05
Fundamental theorem of arithmetic unique-factorization-theorem, unique-prime-factorization-theorem	084HH1NDCB	statement	W1	11A51
P-adic valuation of a product	0850JJMJYZ	statement	W0	11A51
Angle bisector theorem	0859R2V6ES	statement	W1	51M04
Jordan normal form jordan-canonical-form	085HQ5G5TE	statement	W1	15A21, 15A20
Law of quadratic reciprocity quadratic-reciprocity	085MJS6907	statement	W1	11A15
Fermat's right triangle theorem	086BE0J3FZ	statement	W1	11D25
Mean of the Poisson distribution	086HEVXR9Z	statement	W0	60E05
Chevalley–Warning theorem	08895Q5W96	statement	W0	11T06
Divergence part of the ratio test	08AM0KRCZ1	statement	W0	40A05
Class equation class-formula	08BPSC6YTE	statement	W0	20E45
Product of primitive polynomials is primitive	08C1NWBNHA	statement	W0	13F20
Existence of an eigenvalue over an algebraically closed field	08CJB2NQ92	statement	W0	15A18
Product of cyclic groups is cyclic iff the orders are coprime	08FDFEF8D1	statement	W0	20K01
Homomorphisms preserve identity and inverses	08FKQD7NJ3	statement	W0	20A05
Product of countable sets is countable	08G4XH86JC	statement	W0	03E10
Tutte's theorem	08J7R35B6Q	statement	W1	05C70
Distributive laws for sets distributivity-of-union-and-intersection	08N6EVA7DV	statement	W0	03E20
Product formula for the order of HK	08PY4GNAPK	statement	W0	20D60
Picard's great theorem big-picard-theorem, great-picard-theorem	08QA8QTM71	statement	W0	30D35
Independence means the joint law is the product of the marginals	08QCA2F1NX	statement	W0	60A05
Number of functions between finite sets	08QQH9F7G0	statement	W0	05A05
Order of an element divides the order of the group	08V7JHS3QZ	statement	W0	20D60
Power series of cosine	08W5RN375X	statement	W0	33B10, 30B10
Hall's marriage theorem	08WCB90WND	statement	W0	05D15
Cauchy–Binet formula	08WE2W7DYS	statement	W1	15A15
Euler's four-square identity	08WTN6SCQ6	statement	W0	11E25
An iterate of the Picard operator is a contraction	08XDXP86XE	statement	W0	34A12, 47H10
Integration by parts	08Y1BBQTK9	statement	W1	26A42
Subfields of a finite field	08YERZDM9X	statement	W0	12E20
Steinitz exchange lemma replacement-theorem	08ZDRN6H41	statement	W0	15A03
An injective endomorphism of a finite-dimensional space is surjective	0912EEEVCT	statement	W0	15A04
Euler's identity	09285XX7AE	statement	W1	33B10
Minimal polynomial divides the characteristic polynomial	093X6MN6Y6	statement	W0	15A18
In a PID a nonzero element is irreducible iff it generates a maximal ideal	095ZHQ7WCJ	statement	W0	13F10
Unique paths in trees	096B7Q5742	statement	W0	05C05
Geometric solutions come from roots of the characteristic polynomial	096SD4ERQH	statement	W0	39A06
Linearly independent set of the right size is a basis	096V7H13H9	statement	W0	15A03
Cramer's rule	0977KZ6PQB	statement	W1	15A06, 15A15
Riesz's lemma riesz-lemma	097C7KCAT5	statement	W0	46B20
Intermediate value theorem for connected spaces intermediate-value-theorem	098C0KZZAP	statement	W0	54D05
Fixed points of a p-group action	098D2E7DEH	statement	W0	20D15, 20B05
Peano existence theorem cauchy-peano-theorem, peano-theorem	098YP831QY	statement	W1	34A12
Power series of the complex logarithm mercator-series, newton-mercator-series	09BG0Y7SZD	statement	W0	30B10
Area of a region as a line integral area-by-greens-theorem	09CBQB6V67	statement	W0	26B20
Open sets characterised by neighbourhoods	09CJ00H3NW	statement	W0	54A05
Coordinates in an orthonormal basis	09DZ8CD1AK	statement	W0	15A63, 46C05
Trace of a transpose	09E1RCZ7YT	statement	W0	15A15
Epsilon-N definition of the limit of a sequence	09G6KHS6GY	statement	W0	40A05
Second Sylow theorem	09GCQ5STVJ	statement	W0	20D20
Transpose of a product	09GK5PS824	statement	W0	15A99
Closed sets contain their limits	09GQ3ZTQJ9	statement	W0	54E35
Completeness of the space of bounded continuous functions	09GRCZVR5E	statement	W0	54C35
Euler's polyhedron formula euler-formula-for-polyhedra	09HT3P35YP	statement	W0	52B10
Sum of the totient over the divisors gauss-totient-sum	09JXE6XMCC	statement	W0	11A25
Groups of order p squared are abelian	09JZ9P4899	statement	W0	20D15
Ring homomorphisms from a field are injective	09N7DZ7SDB	statement	W0	12E99
Finite intersection of open sets is open	09NDE9V7X1	statement	W0	54E35
De Morgan's laws de-morgan-laws	09PKJKA6J0	statement	W1	03B05
Mean of the normal distribution	09PR1V6RWR	statement	W0	60E05
Liouville's formula abel-jacobi-liouville-identity	09PS3S0EF6	statement	W0	34A30
Cancellation in congruences	09RDZZGJZ9	statement	W0	11A07
The rationals form an ordered field	09RFKMBQ63	statement	W0	12J15
Every walk contains a path	09VZBHB33V	statement	W0	05C38
Permuting rows multiplies the determinant by the sign	09YB3WQG38	statement	W0	15A15
Divisibility by 11	09YBMJTNBM	statement	W0	11A63
Intersection of closed sets is closed	09YMV8H4X5	statement	W0	54E35
The number of Sylow subgroups is the index of the normaliser	09ZJ6CAK7S	statement	W0	20D20
Product of compact sets is compact	09ZKE5XQ74	statement	W0	54D30
Determinant of a matrix exponential	0A1QQN333A	statement	W0	15A16, 15A15
Open sets of a metric space	0A26X79RTB	statement	W0	54E35
The reals are Archimedean	0A3GWZ86AY	statement	W0	26A03
Derivative gives the directional derivatives	0A6PMR20N4	statement	W0	26B05
Archimedean property	0A74SX55QP	statement	W0	12J15
Baire category theorem	0A7KGAYHGV	statement	W1	54E52
Tower law multiplicativity-formula-for-degrees	0A7KJ68XHT	statement	W0	12F05
Chain rule for a composition with a curve	0A8TJ0VHC7	statement	W0	26B05
Schröder–Bernstein theorem cantor-bernstein-theorem, cantor-schroeder-bernstein-theorem	0A9V6RKQG6	statement	W1	03E10
Finite-dimensional normed spaces are complete	0ABP2F2ZP7	statement	W0	46B99
Metrizable spaces are normal	0AD0BZ49DW	statement	W0	54E35
If G modulo its centre is cyclic then G is abelian	0AH9Q6YNMT	statement	W0	20A05
Stokes' theorem kelvin-stokes-theorem	0AKRKVHW94	statement	W1	26B20
Gram matrices are positive semidefinite	0AM050KCAW	statement	W0	15B57, 15A63
Cauchy product of absolutely convergent series	0AN28XQ45Z	statement	W0	40A05
Second isomorphism theorem for vector spaces	0APN65D6Y6	statement	W0	15A03, 16D10
The symmetric group is generated by transpositions	0AQNX7G443	statement	W0	20B30
Differentiation under the integral sign leibniz-integral-rule	0AR06W1E1B	statement	W1	26B15
Simplicity of the alternating group	0ARPRJQWZ2	statement	W0	20B30, 20D06
The Möbius function is the inverse of the constant function 1	0ASC73QEQT	statement	W0	11A25
Boundedness theorem	0ATVXC3NCC	statement	W0	26A15
R/P is an integral domain iff P is prime	0AVXBEC05W	statement	W0	13A15
Totient of a prime power	0AVY8HKBGD	statement	W0	11A25
K[x]/(f) is a field iff f is irreducible	0AWMPX35CW	statement	W0	12E05
Completeness axiom least-upper-bound-property, supremum-property, dedekind-completeness	0AXWET80YW	statement	W0	26A03
Moment-generating function of the normal distribution	0B1G4E21G7	statement	W0	60E10
Curl-free vector field on a convex set is conservative poincare-lemma-for-vector-fields	0B22P010D6	statement	W0	26B12
Open balls are open	0B2305GNAZ	statement	W0	54E35
R[x] is an integral domain iff R is	0B5Z1EC66J	statement	W0	13F20
Legendre's three-square theorem	0B64Q7XNE3	statement	W0	11E25
Continuity via closed sets	0B8GPXFSP7	statement	W0	54C05
Cauchy condensation test	0B96KMDDD1	statement	W1	40A05
Connected subsets of the real line are intervals	0B9ZQFMQNV	statement	W0	54D05
Mean value theorem lagrange-mean-value-theorem	0BARQY52N5	statement	W1	26A24
Matrix determinant lemma	0BC3Q6K92H	statement	W0	15A15
Order of the Galois group of a Galois extension equals its degree	0BDJBH8B4Z	statement	W0	12F10
Solutions for complex conjugate roots	0BEZX8F2XW	statement	W0	34A30
Global existence for globally Lipschitz vector fields	0BFD3A6CRH	statement	W0	34A12
Weak law of large numbers khinchin-law, bernoulli-law-of-large-numbers	0BFDHF2H7N	statement	W0	60F05
Number of k-element subsets	0BFMR2FQ8B	statement	W0	05A10
Path independence of line integrals conservative-iff-path-independent	0BFN21TF5F	statement	W0	26B20
A linear map is injective iff its kernel is trivial	0BJBYCGMWE	statement	W0	15A04
Mertens' theorem on Cauchy products	0BJSWZJG18	statement	W0	40A05
Hölder's inequality for sums	0BKDAGMGX9	statement	W0	26D15
Fermat's little theorem in the form a^p = a	0BMXWXDVJZ	statement	W0	11A07
Trees are bipartite	0BN2A6EBYA	statement	W0	05C05
Side-side-side congruence sss-congruence	0BRBYRK6PA	statement	W0	51M04
Goursat's theorem goursat-lemma	0BRG85WXYC	statement	W0	30E20
Polar form polar-form-of-a-complex-number	0BRXFNQ5JV	statement	W0	30A99
Quotient rule	0BS0NJPKVE	statement	W1	26A24
Multiplication rule chain-rule-of-probability, general-product-rule	0BS3RMX8HM	statement	W0	60A05
Riemann's theorem on removable singularities riemann-removable-singularity-theorem	0BSQDZWF34	statement	W0	30D30
Pythagorean theorem in an inner product space	0BVTDM872V	statement	W0	46C05
Uniform limits commute with integration	0BWGW68B66	statement	W0	40A30, 26A42
Power series converge uniformly on smaller discs inside the radius of convergence	0BWXV7GADW	statement	W0	30B10, 40A30
Ring of integers	0BXA4Q0JHW	statement	W0	13A99
Implicit function theorem implicit-function-theorem	0BXBADR94C	statement	W1	26B10
Slopes of a convex function are increasing	0BY5FTHEEE	statement	W0	26A51
Generalized pigeonhole principle	0BY7GN3449	statement	W0	05A05
Zero derivative on a connected open set implies constant	0BYZTFM0DJ	statement	W0	26B05
Addition rule for two events inclusion-exclusion-for-two-events	0BZQ6ZX584	statement	W0	60A05
Order of the dihedral group	0BZVNWJ352	statement	W0	20B25
Recurrence for Stirling numbers of the second kind	0C019SDTER	statement	W0	11B73
Laplace expansion along a row cofactor-expansion	0C08BQ3M05	statement	W0	15A15
Linear maps on finite-dimensional spaces are continuous	0C13E623WD	statement	W0	47B01
Determinant is the product of the eigenvalues	0C2F40MEBC	statement	W0	15A15, 15A18
Associativity of addition	0C32J27WQC	statement	W0	03F30
Euler product formula	0C3PN4075R	statement	W0	11M06
Eigenvalues of a self-adjoint operator are real	0C4NT4GT3X	statement	W0	47B15, 15A18
Inclusion–exclusion for two sets	0C4YEQ9H5E	statement	W0	05A05
Recurrence for Stirling numbers of the first kind	0C5BFX94J9	statement	W0	11B73
Number of subsets of a finite set	0C5RDJE73X	statement	W0	05A05
Polynomial functions are continuous	0C5TP6RYSV	statement	W0	26A15
Reverse triangle inequality	0C9S13WKMF	statement	W0	26A03
The kernel is a normal subgroup	0C9ZKYSPYR	statement	W0	20A05
A finite field of order q is the splitting field of x^q - x	0CDAHW576M	statement	W0	12E20
Degrees along an Eulerian trail	0CDVDGWGEG	statement	W0	05C45
Universal property of the free group	0CDWKDYWN6	statement	W0	20E05
Number of permutations	0CEBCS0E0E	statement	W0	05A05
Classification of complex quadratic forms	0CEX9BRXRZ	statement	W0	11E04, 15A63
exp(2 pi i/n) is a primitive root of unity	0CF0XGYHNJ	statement	W0	11R18
Division algorithm euclidean-division, division-with-remainder	0CHQKZFK5S	statement	W0	11A05
Finite subgroups of the multiplicative group of a field are cyclic	0CKGBEJX6B	statement	W0	12E20
Abel's test	0CN97GADE5	statement	W1	40A05
Impossibility of doubling the cube	0CQ357M0QS	statement	W0	12F05
Uniform convergence of derivatives allows term-by-term differentiation	0CS42KEM5C	statement	W0	40A30, 26A24
Exponential growth beats polynomial growth	0CT6CBGTYY	statement	W0	26A12, 33B10
First isomorphism theorem fundamental-theorem-on-homomorphisms	0CXXJNG5B6	statement	W0	20A05
Linearity of the derivative	0CXZ217QDP	statement	W0	26B05
Derivative of a continuous linear map	0CYYAF8AD2	statement	W0	26B05
Fibonacci recurrence	0D0SMQYEJA	statement	W0	11B39
Correspondence theorem for rings fourth-isomorphism-theorem-for-rings, lattice-theorem-for-rings	0D1R4SVMBQ	statement	W0	16D25
A set is closed iff it equals its closure	0D2W7FS52T	statement	W0	54A05
Integration by substitution change-of-variables-formula	0D37QFPEZE	statement	W1	26A42
Consecutive Fibonacci numbers are coprime	0D3PFXEAKF	statement	W0	11B39
Rouché's theorem rouche-theorem	0D430QR02W	statement	W1	30C15
A continuous injective function on an interval is strictly monotone	0D6FCW80A0	statement	W0	26A48
Polynomial ring over a UFD is a UFD	0D6KH8Y59N	statement	W0	13F15
Zero is not a successor	0D752BG155	statement	W0	03F30
The exponential function is convex	0D7GRZ2ADX	statement	W0	26A51
Variance of a sum	0D86GJEZ39	statement	W0	60A05
Limits are unique in Hausdorff spaces	0D8T984XEE	statement	W0	54D10
Uniqueness of inverses	0D9NDGE9KP	statement	W0	20A05
Mean of the geometric distribution	0DB0R4N5XX	statement	W0	60E05
Matrix of the adjoint is the conjugate transpose	0DBTE6HVBD	statement	W0	15A04, 47A05
Strong law of large numbers kolmogorov-strong-law	0DFWHQ839T	statement	W0	60F15
Finite extensions are algebraic	0DFYTNZ6AM	statement	W0	12F05
Commutativity of addition	0DFZNHJ0S2	statement	W0	03F30
Cauchy's integral formula cauchy-integral-formula	0DG10TVYPN	statement	W1	30E20
Spectral theorem for Hermitian matrices	0DGZBQWZWN	statement	W0	15A18, 15B57
Order of a permutation is the lcm of its cycle lengths	0DH7HMXP9F	statement	W0	20B30
Estimation lemma ml-inequality, ml-lemma	0DJMGPN8K9	statement	W0	30A10
Cosets have the same cardinality as the subgroup	0DKMBWTD7P	statement	W0	20A05
Basel problem sum-of-reciprocals-of-squares	0DMY75D6FV	statement	W1	40A05
K[x] is a Euclidean domain	0DQG39K2NH	statement	W0	13F07
Universal property of the polynomial ring	0DQMDSVSXJ	statement	W0	13F20
Bézout's identity bezout-lemma, bezouts-lemma	0DQVHMYAGA	statement	W1	11A05
Inequality of arithmetic and geometric means am-gm-inequality	0DRF0F3XC9	statement	W0	26E60
The rationals are countable	0DS9KWFDK2	statement	W0	03E10
Stone's representation theorem for finite Boolean algebras	0DYS9C3HH5	statement	W0	06E05, 06E15
Irrationality of the square root of 2	0DZGSDHD92	statement	W0	11J72
Number of nth roots of unity	0E021GF2B8	statement	W0	11R18
Jordan–Hölder theorem jordan-holder-theorem	0E088ZP533	statement	W0	20E15, 20D30
Primitive root theorem	0E0DNQK22P	statement	W0	11A07
Orbit-stabiliser theorem orbit-stabilizer-theorem	0E2HSCKZ6C	statement	W0	20B05
Dimension of the orthogonal complement	0E2NYPVSP9	statement	W0	15A03, 46C05
Law of total probability rule-of-elimination	0E5G5FMT2R	statement	W0	60A05
Convergents converge to the number	0E70M92FE3	statement	W0	11A55
Fermat's Last Theorem for n = 4	0E741HSMJ1	statement	W0	11D25
Riemann rearrangement theorem riemann-series-theorem	0E7VBYGFF7	statement	W1	40A05
Exponential of a sum	0E8HNVBCSP	statement	W0	33B10
Harmonic series diverges	0E9M24KS9J	statement	W0	40A05
Chain rule in several variables multivariable-chain-rule	0EAAS2EHDR	statement	W0	26B05
A composite number has a prime factor at most its square root	0EB6BBMQMC	statement	W0	11A51
A finite integral domain is a field	0EBE031B8E	statement	W0	13G05
The multiplicative group of a finite field is cyclic	0EBZ3G455G	statement	W0	12E20
Existence of the infimum	0EDH403M21	statement	W0	26A03
Neyman–Pearson lemma neyman-pearson-lemma	0EE19CFEEF	statement	W1	62F03
Rule of sum addition-principle, sum-rule	0EE2V3CHFK	statement	W0	05A05
Boole's inequality union-bound	0EGSEE9J9R	statement	W1	60E15
Prime number theorem	0EHBY5Y84N	statement	W1	11N05
Liouville's theorem liouvilles-theorem-complex-analysis	0EHKVRF4J6	statement	W1	30D20
Binomial theorem	0EHWPWGHB2	statement	W1	05A10
Universal property of the abelianisation	0EJ4PC8NJ6	statement	W0	20F12
Epsilon-delta continuity in metric spaces	0EKGKY5TGH	statement	W0	54E35
Existence of nontrivial solutions of Pell's equation	0EM6C9SZN5	statement	W0	11D09
Inverse in terms of the adjugate	0ENVM493VK	statement	W0	15A09
Continuous image of a connected set is connected	0EPD87YVG8	statement	W0	54D05
Convergence in probability implies convergence in distribution	0EPTDZPJ83	statement	W0	60F05
Central limit theorem clt, lindeberg-levy-central-limit-theorem	0EPZC4Z1FC	statement	W1	60F05
QR decomposition	0ERWG4NXQ9	statement	W1	15A23, 65F25
Divisibility by 9	0ESHD7ZQDX	statement	W0	11A63
Existence of an algebraic closure	0ETGBAK2CC	statement	W0	12F05
Gershgorin circle theorem	0ETGP0XVCJ	statement	W1	15A42, 15A18
Poincaré–Bendixson theorem	0EW1X61ZT1	statement	W0	34C05, 37C27
Impossibility of trisecting the angle	0EWXPZCSZ0	statement	W0	12F05
The exponential function is its own derivative	0EX9GFJ0B3	statement	W0	33B10, 26A24
Cantor's intersection theorem	0EZBG8SKJM	statement	W1	54D30
Cauchy's integral formula for derivatives cauchy-differentiation-formula	0F0H5P5DED	statement	W0	30E20
Prime elements are irreducible in an integral domain	0F0K8DB9TD	statement	W0	13A05
Superposition principle	0F2VBPXNP9	statement	W0	34A30
Bounded linear maps are continuous	0F3K4C7XYW	statement	W0	47B01
Derivative vanishes at a local extremum fermat-theorem-several-variables, interior-extremum-theorem-several-variables	0F405477F8	statement	W0	26B05
Divergence of a curl is zero div-curl-vanishes	0F56CMMC5P	statement	W0	26B12
g to the n equals 1 iff the order divides n power-is-identity-iff-order-divides	0F5QC101Q7	statement	W0	20A05
Cayley–Hamilton theorem	0F765KFC2J	statement	W1	15A24, 15A18
Closed subsets of complete spaces are complete	0FBXJZX3MK	statement	W0	54E50
The gamma function extends the factorial	0FDCW77H44	statement	W0	33B15
A subgroup whose index is the smallest prime divisor of the order is normal	0FEBE9NC0E	statement	W0	20D60
e as the limit of (1 + 1/n)^n	0FEMF8JKAF	statement	W0	26A09
Universal property of the quotient topology	0FF2FJ8CH2	statement	W0	54B15
Inclusion–exclusion principle	0FF7726C7P	statement	W1	05A05
The reals form a field	0FGENPMPJX	statement	W0	12D99
Characterization of bridges	0FHM8DB6PM	statement	W0	05C40
Epsilon-delta uniform continuity	0FHSDCQACY	statement	W0	54E40
Chromatic number of a complete bipartite graph	0FJBBCXYPS	statement	W0	05C15
Bertrand's postulate bertrand-chebyshev-theorem, chebyshev-theorem	0FJTGZA4GS	statement	W1	11N05
Triangle inequality for norms	0FJZMBX0ZZ	statement	W0	46B20
Simultaneous diagonalisation	0FK17N4DKA	statement	W0	15A20, 15A27
Monotone convergence theorem for sequences	0FM6N4R0VB	statement	W1	40A05
Burnside's p^a q^b theorem burnsides-theorem	0FMAQSB1SC	statement	W0	20D10
Chinese remainder theorem	0FNN9B4W64	statement	W1	11A07
Lévy's continuity theorem levy-continuity-theorem	0FPWF7TTMB	statement	W0	60E10, 60F05
Inverse of a complex number	0FQRAV5SKH	statement	W0	12D99
Comparison test for improper integrals	0FR1BDKK10	statement	W0	40A10
Heron's formula heros-formula	0FRBZ2X4HJ	statement	W1	51M25
The complex numbers form a field	0FRSR10DWF	statement	W0	12D99
Trace is a coefficient of the characteristic polynomial	0FRYPZ6D0X	statement	W0	15A15, 15A18
Infinite pigeonhole principle	0FS3RHF6KE	statement	W0	05A05
Determinant of a matrix with a zero row	0FS6B46E5T	statement	W0	15A15
Bertrand's ballot theorem	0FS972T0ZH	statement	W1	05A15
Reversing a path changes the sign of a line integral orientation-reversal-of-line-integrals	0FSCXYG856	statement	W0	26B12
Multiplicativity of the totient function	0FSJA9M43W	statement	W0	11A25
Second derivative test	0FZFHK97P7	statement	W0	26A24
Transcendence of pi lindemann-s-theorem	0G0F7FGCGP	statement	W0	11J81
Sylvester's determinant theorem weinstein-aronszajn-identity	0G24VQ1088	statement	W0	15A15
The complex exponential is entire	0G2YJN0H5S	statement	W0	33B10
Continuous dependence on initial data	0G3DBXRRQJ	statement	W0	34A12
Automorphism group of a cyclic group	0G4C8SJ6PV	statement	W0	20F28
Derivative of the inverse function inverse-derivative-formula	0G65751VSW	statement	W0	26B10
Cauchy sequences are bounded	0G6D8E7CTA	statement	W0	40A05
Uniqueness of the complete ordered field	0G8G1TH5WK	statement	W0	12J15
Inscribed angle theorem central-angle-theorem	0GA1V8NN8C	statement	W0	51M04
Derivative of arcsine	0GA6G43EA9	statement	W0	33B10, 26A24
Epsilon-delta definition of a limit	0GBZDAFPX8	statement	W0	26A03
Induction from an arbitrary base case	0GF6AJEBZ0	statement	W0	03F30
General solution of an inhomogeneous linear equation	0GHWEH6H15	statement	W0	34A30
Universal property of the quotient group factorization-through-the-quotient	0GJ83E78A5	statement	W0	20A05
Cancellation in an integral domain	0GJM24EXP9	statement	W0	13G05
Trace is linear	0GJWQZCPZM	statement	W0	15A15
Addition formulas for hyperbolic functions	0GJZCE87WP	statement	W0	33B10
Solution space of a homogeneous linear equation has dimension n	0GK68PZ6KH	statement	W0	34A30
Absolute value is multiplicative	0GMV7GP8W0	statement	W0	26A03
Nilpotent groups are solvable	0GNG2KVPZJ	statement	W0	20F18, 20F16
Dirichlet's theorem on arithmetic progressions dirichlet-prime-number-theorem	0GNVN3CA2P	statement	W1	11N13
Cardinality of the power set	0GPFKS96T7	statement	W0	03E10
The medians meet at the centroid	0GPQ67XV7N	statement	W0	51M04
Quotient of continuous functions is continuous	0GR2APWTAC	statement	W0	26A15
Angles in the same segment are equal	0GS0AW6JRY	statement	W0	51M04
Thales's theorem	0GSDHYMA1T	statement	W1	51M04
Cavalieri's principle method-of-indivisibles	0GTZ2F3PQY	statement	W1	28A75
Bijection principle	0GV2573FP4	statement	W0	05A19
Fundamental theorem of symmetric polynomials	0GW1ZZH0R4	statement	W0	05E05
Integral of sine	0GXCXCX3QN	statement	W0	26A36
Units of Z/nZ are the residues coprime to n	0GXNHEHQNA	statement	W0	11A07, 20K01
Second derivative test in several variables second-partial-derivative-test	0GYDV9FE98	statement	W0	49K10
Divergence theorem on a rectangle in the plane planar-divergence-theorem-rectangle	0GZ3D8F921	statement	W0	26B20
The order of a finite field is a prime power	0H5WWC8RZX	statement	W0	12E20
Taylor's theorem with the Lagrange remainder	0H5ZAZCX2T	statement	W0	41A80
Changing the order of integration reversing-order-of-integration	0H60H1Q0SX	statement	W0	26B15
Product of power series	0H6KWAYS87	statement	W0	13F25
Every finite tree with at least two vertices has a leaf	0H8Q4MANBD	statement	W0	05C05
Rule of Sarrus	0H8SZFFDXJ	statement	W0	15A15
Interior is the largest open subset	0HAZEFH137	statement	W0	54A05
Induction on the integers	0HBS1F00DN	statement	W0	11A99
Union of open sets is open	0HEF46RPEK	statement	W0	54E35
Russell's paradox russell-paradox	0HESMMSYEG	statement	W1	03E30
Pigeonhole principle	0HGVCWQGY3	statement	W1	05A05
Solutions for distinct real roots	0HJ0HDA6W7	statement	W0	34A30
Second isomorphism theorem for rings	0HJ4DTW6FN	statement	W0	16D25
A sequence converges iff its liminf and limsup agree	0HM732ZNVC	statement	W0	40A05
Eigenvectors with distinct eigenvalues are linearly independent	0HNMFG8F8K	statement	W0	15A18
Generalised Stokes theorem stokes-cartan-theorem	0HPHKCGEQ0	statement	W0	58C35
Green's theorem	0HR3N02317	statement	W1	26B20
Solutions for repeated roots	0HRVY67CNV	statement	W0	34A30
Axiom of choice ac, axiom-of-choice	0HTGB13FE2	statement	W1	03E25
Rouché–Capelli theorem kronecker-capelli-theorem	0HV1SKWPMS	statement	W0	15A06
Limit comparison test	0HW7BNHHGF	statement	W1	40A05
Totient of a prime	0HY1MXMEN9	statement	W0	11A25
Eigenvalues of a positive definite matrix are positive	0HYC2RHD3M	statement	W0	15B57, 15A18
Injective iff it has a left inverse	0HYFEEZAEM	statement	W0	03E20
Modulus is multiplicative	0HYNZE940T	statement	W0	30A99
Mean value property mean-value-property-of-harmonic-functions, gauss-mean-value-theorem	0HYPR64JM2	statement	W0	31A05
Solutions of Pell's equation are powers of the fundamental solution	0J1TT091TN	statement	W0	11D09
Polar decomposition	0J2C7BDJQA	statement	W1	15A23
Conjugacy classes of the symmetric group correspond to cycle types	0J438GAC8K	statement	W0	20B30
The symmetric group on five or more letters is not solvable	0J53NE674D	statement	W0	20F16, 20B30
Congruence is compatible with powers	0J5VGJYYC3	statement	W0	11A07
Intersecting secants theorem secant-theorem	0J5XR7BW2S	statement	W0	51M04
Lyapunov's stability theorem lyapunov-direct-method	0J6A752DTZ	statement	W0	34D20
Associativity of composition composition-is-associative	0J6AKYZQT8	statement	W0	03E20
Kuratowski's theorem	0J6G5NJC5R	statement	W0	05C10
Rearrangements of an absolutely convergent series have the same sum	0J76TP9FGD	statement	W0	40A05
Logarithm of a quotient	0J7PHRBNNS	statement	W0	33B10
Sperner's theorem	0J87V9K1GE	statement	W1	05D05
Taylor's theorem in several variables multivariate-taylor-theorem	0J8T4K4YTE	statement	W0	26B12
Determinant of a block triangular matrix	0J9TVTNB4K	statement	W0	15A15
Ratio formula for the radius of convergence	0JBMYAA9QH	statement	W0	30B10
Vector calculus identities product-rules-for-grad-div-curl	0JC5X4HWR2	statement	W0	26B12
Sign is a homomorphism	0JEJJCB0EX	statement	W0	20B30
The cumulative distribution function determines the distribution	0JEVZAFDY6	statement	W0	60E05
Turán's theorem	0JG1KZSPFZ	statement	W0	05C35
Eigenspaces of a self-adjoint operator are orthogonal	0JHGAV9H25	statement	W0	47B15, 15A18
Cauchy's estimates cauchy-inequalities, cauchy-estimate	0JJRENWMP6	statement	W0	30A10
Abelian simple groups have prime order	0JJV80RXHD	statement	W0	20E32, 20K01
Cauchy's theorem cauchys-theorem-group-theory	0JM7PA288B	statement	W0	20D20
Lindemann–Weierstrass theorem	0JNCBFMPXR	statement	W1	11J81
Convolution theorem for the Laplace transform	0JNMJEDD93	statement	W0	44A10, 44A35
Fundamental theorem of algebra dalembert-gauss-theorem, dalemberts-theorem	0JP0W07Y9A	statement	W1	12D10
Kőnig's theorem	0JP0ZF57PN	statement	W1	05C70
Subgroups of abelian groups are normal	0JPDTEDCFD	statement	W0	20A05
Order of the general linear group over a finite field	0JQ1KNQW2K	statement	W0	20G40
Weierstrass approximation theorem	0JQE130DHW	statement	W0	41A10
Estimate for approximate solutions	0JTPMCCZT2	statement	W0	34A12, 34A45
Tychonoff's theorem tychonoff-theorem	0JTRSJKCFB	statement	W1	54D30
An orthonormal family is linearly independent	0JWM6GJNQW	statement	W0	15A63, 46C05
L'Hôpital's rule lhopital-rule, bernoulli-rule	0JWT4PPQ7B	statement	W1	26A24
Divergence theorem gauss-theorem, gauss-ostrogradsky-theorem	0JX86PSSA9	statement	W1	26B20
Legendre's theorem on continued fractions	0JXTQ392ZM	statement	W0	11J70
Lifting-the-exponent lemma lte-lemma	0JYF6PTKEW	statement	W1	11A51
Power rule	0JZGW75C5Z	statement	W1	26A24
Laplace transform of a derivative	0K090GVHVN	statement	W0	44A10
Distance from a point to a plane	0K1E2S6Z69	statement	W1	51N20
Lipschitz functions are uniformly continuous	0K1EWAR6AF	statement	W0	26A16
Determinant of a triangular matrix	0K1KKMFHYH	statement	W0	15A15
Integral of 1/x	0K1N1Y4EGZ	statement	W0	26A36
Brahmagupta–Fibonacci identity diophantus-identity	0K2DMACEZ4	statement	W0	11E25
Logarithm of a product	0K2FNY6DYV	statement	W0	33B10
Minkowski's theorem minkowski-convex-body-theorem	0K387S2PKQ	statement	W0	11H06
Factor theorem	0K3MWA7DMC	statement	W1	13F20
Determinant of a matrix with two equal rows	0K4VQB7HWR	statement	W0	15A15
Complement of an open set is closed	0K67Q60Z8P	statement	W0	54A05
Isolated zeros theorem principle-of-isolated-zeros, zeros-are-isolated	0K83KEJ43P	statement	W0	30C15
Compactness and sequential compactness agree in metric spaces	0K8SGQSV7G	statement	W0	54E45
Continuous image of a compact set is compact	0K9AAJ8G51	statement	W0	54D30
Inverse function theorem inverse-mapping-theorem	0K9HSJFCMJ	statement	W1	26B10
General Leibniz rule	0K9QCK6WJC	statement	W1	26A24
Determinant via the Schur complement	0KA7A4ENVJ	statement	W0	15A15
Sum of binomial coefficients	0KAMF19NV8	statement	W0	05A10
Subgroups of cyclic groups are cyclic	0KB1ND7XDS	statement	W0	20K27
Distributive law distributivity-of-multiplication-over-addition	0KBEMAJAYA	statement	W0	03F30
Stirling's formula stirling-approximation	0KC0F51T6A	statement	W1	41A60, 05A10
Bolzano–Weierstrass theorem	0KDJD249DT	statement	W1	40A05
Classification of Pythagorean triples euclid-formula	0KF3J2KAER	statement	W0	11D09
The alternating group is generated by three-cycles	0KFZ0QX83G	statement	W0	20B30
A polynomial over a field has at most as many roots as its degree	0KJVQV3E0F	statement	W0	12E05
One-sided limits of a monotone function exist	0KJXHN0TW0	statement	W0	26A48
Hausdorff maximal principle maximal-chain-principle	0KM4KVR9MV	statement	W1	03E25
Determinant of a linear map is the determinant of its matrix	0KMN32XGPF	statement	W0	15A04, 15A15
Strong induction complete-induction, course-of-values-induction	0KMVFSHFGZ	statement	W0	03F30
The exponential function is strictly increasing	0KN2V7840E	statement	W0	33B10
Ceva's theorem	0KN93VDSXA	statement	W1	51M04
Variance under scaling	0KVQ9D86BM	statement	W0	60A05
Reduction modulo p test for irreducibility	0KWWEXW0RN	statement	W0	12E05
Radius of convergence of the binomial series	0KX1MXJ5MR	statement	W0	30B10
Continuous partial derivatives imply differentiability	0KXSK8TEEB	statement	W0	26B05
Derivative of x^a	0KY08TWDMQ	statement	W0	26A24, 26A09
Lagrange's four-square theorem	0KYYSMEVHH	statement	W1	11E25
Quadratic formula	0KYZXYDGQZ	statement	W1	12D10
Derivative of an inverse function inverse-function-rule	0M0RZ3HSB0	statement	W1	26A24
Linearity of differentiation sum-rule-for-derivatives	0M0TKFRX2A	statement	W0	26A24
Intercept theorem basic-proportionality-theorem, thales-theorem-on-proportions	0M1GFS6PVA	statement	W0	51M04
Bernoulli's inequality	0M1MX28VXK	statement	W1	26D05
Fermat's little theorem	0M25PRN3WQ	statement	W1	11A07
Curl of a gradient is zero curl-grad-vanishes	0M2JRW1J0N	statement	W0	26B12
Cayley's formula	0M2SSGSYPE	statement	W0	05C30
The number of Sylow subgroups divides the index	0M3PYJ3TSE	statement	W0	20D20
Four colour theorem	0M406JC8J1	statement	W1	05C15, 05C10
Every linearly independent set extends to a basis	0M4SXE5WW3	statement	W0	15A03
Classification of the Platonic solids	0M4TCS0RRG	statement	W0	51M20
Existence of inverses modulo n	0M67FWZWPQ	statement	W0	11A07
The only ideals of a field are zero and the whole field	0M6G75E95E	statement	W0	12E99
Universal property of the product topology	0M6W4XNST6	statement	W0	54B10
Euler's criterion	0M7DEDKSYB	statement	W1	11A15
Vieta's formulas	0M8EWQJ1YV	statement	W1	12D10
Approximation property of the supremum	0M8TGGP9JP	statement	W0	26A03
Schwarz lemma schwarzs-lemma	0MB48XDBY3	statement	W1	30C80
Monotonicity of the integral	0MBWQKM8QR	statement	W0	26A42
A finite abelian group is cyclic iff its exponent equals its order	0MC0AQZSHE	statement	W0	20K01
Orthogonal projection is the closest point	0MCDDSCB9Z	statement	W0	46C05, 65F20
Epsilon characterisation of Cauchy sequences	0MCK8K2D7Z	statement	W0	54E35
Division algorithm for polynomials euclidean-division-of-polynomials	0MES3KS0ZC	statement	W0	13F20
Derivative of a polynomial	0MH1WK89PP	statement	W0	26A24
Wronskian test for linear independence of solutions	0MHE4B1QCQ	statement	W0	34A30
Every sequence has a monotone subsequence	0MHGJRZMTM	statement	W0	40A05
A ring homomorphism is injective iff its kernel is zero	0MMCB8RXGA	statement	W0	16B99
Continuum hypothesis ch	0MN2MER9WN	statement	W1	03E50
Derivative as a little-o approximation	0MN882VJ4P	statement	W0	26B05
Diagonalisable iff the minimal polynomial has distinct roots	0MPAJRB23T	statement	W0	15A20
Compact Hausdorff spaces are normal	0MQQQ5NA2S	statement	W0	54D30
Change of basis formula	0MQXVZEBMT	statement	W0	15A04
A quotient is abelian iff the subgroup contains the commutator subgroup	0MS8QGA6S5	statement	W0	20F12
Test for exactness	0MSCQNFTM8	statement	W0	34A05
First isomorphism theorem for linear maps	0MTBGVZ4XJ	statement	W0	15A04, 16D10
Exponentials dominate powers in sequences	0MVTCFW42K	statement	W0	26A12
A series of nonnegative terms converges iff its partial sums are bounded	0MX1HZBBXJ	statement	W0	40A05
Mantel's theorem	0MXEHSCYCS	statement	W0	05C35
Open connected subsets of R^n are path-connected	0MXN7AFBPE	statement	W0	54D05
Compact subsets of a Hausdorff space are closed	0MYFJVMN7M	statement	W0	54D30
Well-ordering theorem zermelo-theorem, well-ordering-principle	0N109NG5ZX	statement	W1	03E25
Irrationality of square roots of non-squares	0N10YRNNWV	statement	W0	11J72
Completeness via Cauchy sequences	0N1ZWFJDN5	statement	W0	54E50
A homomorphism is injective iff its kernel is trivial	0N2P0XRTDF	statement	W0	20A05
The rationals form a field	0N2WPCC00T	statement	W0	12E99
Limits preserve non-strict inequalities	0N32V0E3XJ	statement	W0	40A05
Liouville's theorem on Diophantine approximation	0N3WFZEFPM	statement	W0	11J68
Classification of conics by the discriminant	0N5NR32NQG	statement	W0	51N20
Degree of a simple extension is the degree of the minimal polynomial	0N5QW9K7MH	statement	W0	12F05
Mean value theorem for integrals	0N91N98EG5	statement	W0	26A42
Ore's theorem	0NACHJYPKW	statement	W0	05C45
Apollonius's theorem	0NAKHQ9XYY	statement	W0	51M04
The integral of a continuous function is an antiderivative	0NC2A3HWGT	statement	W0	26A36
Implicit function theorem for a surjective derivative regular-value-theorem-euclidean	0NE2W2XPQJ	statement	W0	26B10
Double negation law double-negation-elimination	0NFAGWH84K	statement	W0	03B05
The minimal polynomial is irreducible	0NFEG48RDR	statement	W0	12F05
Fundamental theorem of calculus	0NHGY0N0JB	statement	W1	26A42
Bayes' theorem bayes-rule, bayes-law, bayes-formula	0NM6E9VW04	statement	W1	62F15
Variance as the mean of the square minus the square of the mean computational-formula-for-variance	0NMF95YK8W	statement	W0	60A05
Epsilon-net characterisation of total boundedness	0NMGJJ19HD	statement	W0	54E35
Trace is the sum of the eigenvalues	0NMXDCNNKR	statement	W0	15A15, 15A18
Closed formula for Catalan numbers	0NNDQVJ54Q	statement	W0	05A15
Schwarz's theorem for C^2 functions clairaut-theorem, schwarz-theorem	0NNQY8WCW6	statement	W0	26B05
Triangle inequality for integrals	0NR82KMYKD	statement	W0	26A42
Composition of continuous functions is continuous	0NRQPQX3VA	statement	W0	26A15
Connected components are closed	0NRT0E2QT2	statement	W0	54D05
Characteristic function of the normal distribution	0NS0TDA4E2	statement	W0	60E10
Derivative of a map into R^n by components	0NS0X75RS1	statement	W0	26B05
Discrete Grönwall inequality	0NTM3J5MFE	statement	W0	26D15, 39A22
Exterior angle theorem	0NTSE7EREA	statement	W0	51M04
Z/pZ is a field for p prime	0NV6E43P4A	statement	W0	11A07
Multiplicativity of the Legendre symbol	0NW1JP7TBR	statement	W0	11A15
Second Borel–Cantelli lemma converse-borel-cantelli-lemma	0NWXRAMEE7	statement	W0	60F20
Weierstrass M-test	0NX5NWAFC9	statement	W1	40A30
Sum of independent normal random variables sum-of-normally-distributed-random-variables	0NXGPJWNFN	statement	W1	60E05
Theorem on friends and strangers	0NYM0ZGAK9	statement	W1	05C55, 05D10
Angle-angle similarity aa-similarity, aaa-similarity	0NZVJYZVTZ	statement	W0	51M04
Classification of isometries of the plane	0P0XDY9FZN	statement	W0	51F20
Second-order Taylor expansion second-order-taylor-formula	0P30YYZN85	statement	W0	26B12
Negation of a universal statement	0P3A06QNDP	statement	W0	03B10
Sine is 2π-periodic	0P4NQD746K	statement	W0	33B10
A function with bounded derivative is Lipschitz	0P64VE79X3	statement	W0	26A16
Picard–Lindelöf theorem cauchy-lipschitz-theorem, existence-and-uniqueness-theorem	0P6KRD5B7A	statement	W1	34A12
Compactness via open covers	0P6PMJB4MA	statement	W0	54D30
Linearity of expectation expectation-is-linear	0P7PTC8DDE	statement	W0	60A05
Vandermonde determinant	0P84B554AS	statement	W0	15A15, 15B05
The exponential function is positive	0P9BNBW2W3	statement	W0	33B10
Metric spaces are Hausdorff	0P9DCDES73	statement	W0	54E35
Existence of a complementary subspace	0P9T8WHNMH	statement	W0	15A03
Continuity is equivalent to sequential continuity	0PAQM3H57X	statement	W0	26A15
Law of sines sine-rule	0PASQ34GHG	statement	W1	51M04
Order of the symmetric group	0PCKBBMEXC	statement	W0	20B30
Fermat's theorem on stationary points interior-extremum-theorem	0PCVBRV9VJ	statement	W0	26A24
First supplement to quadratic reciprocity	0PHBS78HKT	statement	W0	11A15
Heine–Borel theorem in finite-dimensional normed spaces	0PHT6NBYPB	statement	W0	46B20
Alternating series test leibniz-test	0PK8QH1W1V	statement	W1	40A05
Projections are continuous	0PM88Z9W4M	statement	W0	54B10
Order of an inverse	0PMT9YJZVW	statement	W0	20A05
The continued fraction of a rational number terminates	0PMY0YQYXX	statement	W0	11A55
The Gaussian integers are a Euclidean domain	0PN13BB7BT	statement	W0	11R11
Argument principle cauchys-argument-principle	0PN2BXRS8G	statement	W1	30C15
The constructible numbers form a field closed under square roots	0PN9WMRWT7	statement	W0	12F05
Jordan's lemma jordan-lemma	0PNPG2PP9H	statement	W1	30E20
Interior is open	0PNWCM559P	statement	W0	54A05
Determinant is multilinear in the rows	0PPG793642	statement	W0	15A15
Second isomorphism theorem diamond-isomorphism-theorem	0PPP2J2DJV	statement	W0	20A05
Probability of the complement complement-rule	0PQEBTYDZM	statement	W0	60A05
Alternating sum of binomial coefficients	0PQQGFAWSH	statement	W0	05A10
Principal axis theorem	0PR5P9Z4KM	statement	W0	15A63, 15A18
Dirichlet convolution of multiplicative functions is multiplicative	0PR88XHDMB	statement	W0	11A25
Expectation with respect to the binomial distribution mean-of-binomial-distribution	0PVCTCKD3C	statement	W0	60E05
The exponential series has infinite radius of convergence	0PVJRACB9H	statement	W0	30B10, 33B10
Orthogonal complement of the orthogonal complement	0PXN9G4MX1	statement	W0	46C05
Stolz–Cesàro theorem	0Q3AKZV74D	statement	W0	40A05
Integral of a power	0Q3HYFT9RQ	statement	W0	26A36
Darboux's theorem intermediate-value-theorem-for-derivatives	0Q5A47J48D	statement	W0	26A24
Holomorphic functions with nonzero derivative are conformal holomorphic-maps-are-conformal	0Q7M6K6VD7	statement	W0	30C35
Third Sylow theorem	0Q8DGAZSJ4	statement	W0	20D20
Reciprocal rule	0QD4E5JYPT	statement	W0	26A24
Holomorphic functions are infinitely differentiable	0QEBN8DGVE	statement	W0	30A99
Cayley–Hamilton theorem for linear maps	0QEM68Y0DE	statement	W0	15A04, 15A18
Eigenvalues are the roots of the minimal polynomial	0QF4ZEFG52	statement	W0	15A18
The algebraic numbers form a field	0QFTETCHKB	statement	W0	11R04
Gauss's lemma	0QFV5Y1Z5X	statement	W1	13F20
Irrationality of pi	0QHZX1PK8V	statement	W0	11J72
Dimension of the coordinate space	0QK7FPE6VE	statement	W0	15A03
Euclidean domains are principal ideal domains	0QKVE1GD9A	statement	W0	13F07
The Galois group has order at most the degree	0QM98DNWVW	statement	W0	12F10
Ratio test d-alembert-ratio-test	0QNY6ZBXPN	statement	W1	40A05
Von Dyck's theorem	0QPYHHNRXC	statement	W0	20F05
Derivative of a map into a product	0QQMXFTX0A	statement	W0	26B05
Number of odd-degree vertices is even	0QQQQCPZA8	statement	W0	05C07
In a UFD irreducible elements are prime	0QRCFZKXH8	statement	W0	13F15
Recurrence for derangements	0QRRYXG7V7	statement	W0	05A05
The reals form an ordered field	0QSPNASE50	statement	W0	12J15
The group of units of Z/pZ is cyclic	0QTHB6PE52	statement	W0	11A07, 20K01
Frattini argument frattinis-argument	0QTZDKJEDV	statement	W0	20D20
Dimension of a subspace	0QW084460E	statement	W0	15A03
Every element of a finite field of order q satisfies x^q = x	0QWR8WTZEW	statement	W0	12E20
Tangent–secant theorem	0QX7E9KAAX	statement	W1	51M04
Convergent sequences are Cauchy	0QY87R9CY3	statement	W0	40A05
Continuity of the sum of a uniformly convergent series of functions	0R0MYT0BJD	statement	W0	40A30, 26A15
Fubini's theorem fubini-theorem	0R0T1VWH5X	statement	W1	26B15
Abelian groups are solvable	0R0X73XHAT	statement	W0	20F16
Fraction in lowest terms irreducible-fraction, reduced-fraction	0R64A2CVN4	statement	W0	11A05
Universal property of the quotient ring	0R74MZYNRB	statement	W0	16D25
Compact subsets of a metric space are bounded	0R7BTEWCJ2	statement	W0	54E45
Symmetry of binomial coefficients	0R7JS3DP3W	statement	W0	05A10
pi is greater than 3	0R7SVNYTJS	statement	W0	11Y60
A linear isometry preserves the inner product	0R7VXTYHYZ	statement	W0	15A04, 46C05
Dimension of a tensor product	0R84PF4JV7	statement	W0	15A69, 15A03
A linear map is determined by its values on a basis	0R8X9XA83A	statement	W0	15A04
Integers modulo a prime form a field	0R8YXRC9AJ	statement	W0	11A07
Characterization of the floor	0R9B0B5458	statement	W0	26A09
Divisibility by 3	0R9D4CEJEB	statement	W0	11A63
Gcd of Fibonacci numbers	0R9F850CTH	statement	W0	11B39
Limit of a sum of sequences	0RAM4E07NR	statement	W0	40A05
Bessel's inequality	0RBT5PB74K	statement	W1	46C05
Cesàro means of a convergent sequence converge	0RDRPBMNAC	statement	W0	40G05
Generating function of a sum of independent random variables pgf-of-sum-of-independent-random-variables	0REMT01N36	statement	W0	60E05
Cauchy–Schwarz inequality	0RFWW56Y22	statement	W1	15A63, 46C05
Limit of the cumulative distribution function at infinity	0RJ5TZH6G0	statement	W0	60E05
Logarithm is the inverse of the exponential	0RKW2X63YR	statement	W0	33B10
Cantor set is homeomorphic to the space of binary sequences	0RQ8DHHR8V	statement	W0	54F65
Wedderburn's little theorem	0RRNVX1VKA	statement	W1	12E15
Jensen's inequality	0RWMRTPC87	statement	W1	26D15
Every infinite set has a countably infinite subset	0RWQ5VZ6VQ	statement	W0	03E10
Image of an intersection	0RX7DDBYCK	statement	W0	03E20
Distributivity of matrix multiplication	0RXD6EZYBK	statement	W0	15A99
Chain rule	0RXX2PT1MQ	statement	W1	26A24
Structure theorem for finitely generated abelian groups fundamental-theorem-of-finitely-generated-abelian-groups	0RY0B72XAS	statement	W0	20K25
Lucas's theorem	0RY4GGMEQG	statement	W0	11B65
Law of excluded middle excluded-middle, tertium-non-datur	0RYYK8PG4S	statement	W1	03B05
A nontrivial finite p-group has nontrivial centre	0RZCTT30H5	statement	W0	20D15
Power-reduction formula for cosine	0S049HG1W5	statement	W0	33B10
Size of an orbit times the size of the stabiliser	0S19CWFZM2	statement	W0	20B05
Variation of constants formula for linear systems duhamel-formula	0S1KG0XE40	statement	W0	34A30
Abel's theorem abel-limit-theorem	0S4EMDQS2F	statement	W1	40A30
Convergent sequences are bounded	0S4JF619V7	statement	W0	40A05
Inverse of a product	0S4WTRE9GG	statement	W0	15A09
Order of the group of units of Z/nZ is Euler's totient	0S7495H4HM	statement	W0	11A07, 11A25
Hartman–Grobman theorem linearization-theorem	0S8WX8A4V9	statement	W0	37C15, 34C20
Correspondence theorem lattice-theorem, fourth-isomorphism-theorem	0S9ZVZ34MD	statement	W0	20A05
Derivative of tangent	0SAMR34WXC	statement	W0	33B10, 26A24
Dirichlet convolution formula	0SAR26CKPS	statement	W0	11A25
Gradient theorem fundamental-theorem-of-line-integrals, fundamental-theorem-of-calculus-for-line-integrals	0SD237FEJD	statement	W1	26B20
Product rule in several variables	0SF85PY0QN	statement	W0	26B05
Basis of a tensor product	0SH5VT8QYA	statement	W0	15A69
Closure is the smallest closed superset	0SHC6Z304Z	statement	W0	54A05
Irreducibility of the cyclotomic polynomials over the rationals	0SK1VHZ5R2	statement	W0	11R18
Stability of linear systems via eigenvalues	0SKVEMXJWF	statement	W0	34D20, 34A30
Edge bound for planar graphs	0SM1REAVYJ	statement	W0	05C10
Erdős–Szekeres theorem	0SNJM8HSD3	statement	W1	05A05
A space is the direct sum of a subspace and its orthogonal complement	0SP7P0G7KQ	statement	W0	46C05
Existence of a prime divisor	0SPBEDVNW1	statement	W0	11A41
Change of basis for a bilinear form	0SPYAGE7T0	statement	W0	15A63, 15A21
The Gaussian integers form a Euclidean domain	0SPYEFH7H4	statement	W0	11R11
Principal value of the argument	0SQSQP748R	statement	W0	30A99
Subgroups of the integers	0SRATCFF1W	statement	W0	20K27
Characteristic subgroups are normal	0SRE7K4E49	statement	W0	20F28
Hurwitz's theorem hurwitz-theorem-complex-analysis	0SSKBQN58M	statement	W1	30C15
The degree of a constructible number is a power of two	0SSSM1D475	statement	W0	12F05
Moments are derivatives of the moment-generating function at zero	0STK8KEY9G	statement	W0	60E10
C^1 functions are strictly differentiable continuously-differentiable-implies-strictly-differentiable	0STPPDXGME	statement	W0	26B05
Density of the rationals	0STX0WRDNG	statement	W0	26A03
Almost sure convergence implies convergence in probability	0SVN6X695K	statement	W0	60F15
Primitive element theorem	0SVX98HYV1	statement	W1	12F10
Möbius transformations map circles and lines to circles and lines mobius-maps-preserve-generalized-circles	0SXDHQM2MH	statement	W0	30C35
Dimension of a quotient space	0SXDQ6TN00	statement	W0	15A03
Order of the alternating group	0SZ1KMNWVE	statement	W0	20B30
Determinant is a coefficient of the characteristic polynomial	0T0X8GTYYS	statement	W0	15A15, 15A18
Infinitely many primes congruent to 1 modulo n	0T1BSD7H3M	statement	W0	11N13
Fundamental theorem of Galois theory	0T1Q8D0FW8	statement	W1	12F10
Degree of a product	0T233AZ1GE	statement	W0	13F20
Power series of arctangent gregory-series	0T32ME0A6H	statement	W0	30B10, 33B10
The cross product is perpendicular to its factors	0T4QHJXSD4	statement	W0	15A72
First Borel–Cantelli lemma borel-cantelli-lemma	0T6WS7TT77	statement	W0	60F20
Cauchy–Riemann equations cauchy-riemann-conditions	0T71SSYZ39	statement	W1	30A99
Integration in polar coordinates polar-change-of-variables	0T89W1QZ9K	statement	W0	26B15
The characteristic function determines the distribution uniqueness-theorem-for-characteristic-functions, levy-inversion-formula	0T8BYAFEXX	statement	W0	60E10
Existence of finite fields of every prime power order	0T8M3YC5RG	statement	W0	12E20
Axiom of extensionality extensionality	0TB16T2C97	statement	W1	03E30
The successor function is injective	0TBYMWPWWB	statement	W0	03F30
Dirac's theorem on Hamiltonian cycles	0TC99BRSSB	statement	W0	05C45
C^k function characterised by continuous derivatives	0TCBZMEYGN	statement	W0	26B05
Product of the gcd and the lcm	0TDY6JZHKS	statement	W0	11A05
Remainder theorem polynomial-remainder-theorem	0TEDQH56RW	statement	W1	13F20
Reduction of a higher-order equation to a first-order system	0TH9CPW3VS	statement	W0	34A99
Third isomorphism theorem	0TJ1V9DDPC	statement	W0	20A05
Term-by-term differentiation	0TJ8QBJX5K	statement	W0	40A30, 26A24
Bounded derivative on a convex set implies Lipschitz	0TKG7T3K0E	statement	W0	26B35
An algebraic extension of an algebraic extension is algebraic	0TPWS0K1BC	statement	W0	12F05
Product of a subgroup and a normal subgroup is a subgroup	0TXWV1JGG1	statement	W0	20A05
Characteristic polynomial does not depend on the basis	0TYMASG33Y	statement	W0	15A15, 15A18
Surjective iff it has a right inverse	0TYQNHVB4C	statement	W0	03E20
Row rank equals column rank	0TZAG60ZYT	statement	W0	15A03
Variance of a sum of independent random variables bienayme-formula	0V0778DCW9	statement	W0	60A05
Sign of a cycle	0V0E04DWX2	statement	W0	20B30
Frobenius coin problem coin-problem, frobenius-number	0V11FEXK08	statement	W1	11D07
Derivative of cosine	0V2DV29EGT	statement	W0	33B10, 26A24
Intersection of subspaces	0V33SPH7RR	statement	W0	15A03
Continuous real function on a compact set attains its bounds extreme-value-theorem	0V4DET59NW	statement	W0	54C30
Fibonacci numbers as sums of binomial coefficients	0V4VB6MQDC	statement	W0	11B39
Subgroups of index two are normal	0V547YQRMV	statement	W0	20A05
Logarithm of a power	0V948DE5KA	statement	W0	33B10
First Sylow theorem	0V98WY94B8	statement	W0	20D20
Product rule leibniz-rule-for-products	0V9A43H7WV	statement	W1	26A24
Dirichlet's test	0V9ME8GQE7	statement	W0	40A05
Multiplicativity of the Möbius function	0VB9G5B034	statement	W0	11A25
Kummer's theorem	0VBWK9XYDG	statement	W0	11B65
Euler's theorem fermat-euler-theorem, euler-totient-theorem	0VC4DVE7DQ	statement	W1	11A07
Morera's theorem moreras-theorem	0VDD7W0EKZ	statement	W1	30E20
Volume of a box volume-of-a-rectangular-box	0VEKNG02W0	statement	W0	28A75
Every polynomial has a root in some extension field	0VG02M1FEZ	statement	W0	12F05
Product of continuous functions is continuous	0VGMHCF4SC	statement	W0	26A15
Continuity is equivalent to sequential continuity in metric spaces	0VGPKZ8MRK	statement	W0	54E35
Abel's identity abel-formula	0VGWKX2JHB	statement	W1	34A30
Subsequences of a convergent sequence converge to the same limit	0VHAVXW08V	statement	W0	40A05
Finite-dimensional spaces are isomorphic iff they have equal dimension	0VJBSK15SN	statement	W0	15A03
De Morgan's laws for sets	0VK0W4D5Y5	statement	W0	03E20
Size of a conjugacy class is the index of the centraliser	0VK5V9P8G3	statement	W0	20E45
Banach fixed point theorem contraction-mapping-theorem, banach-fixed-point-theorem	0VK6VEH345	statement	W1	47H10
Lagrange multipliers lagrange-multiplier-theorem, method-of-lagrange-multipliers	0VKKP8X6Q6	statement	W1	90C46
Cartan–Dieudonné theorem	0VMWGYY35Q	statement	W0	51F15, 15B10
If 2^n + 1 is prime then n is a power of 2	0VN4H8M12X	statement	W0	11A41
Polynomials of degree two or three are irreducible iff they have no roots	0VNE161QCK	statement	W0	12E05
Pythagorean theorem pythagoras-theorem	0VP3A1290K	statement	W1	51M04
Rule of product multiplication-principle, product-rule	0VPK4X73Q0	statement	W1	05A05
A tree on n vertices has n − 1 edges	0VSNHTHK8T	statement	W0	05C05
Cancellation laws cancellation-law	0VSNX4P2Q0	statement	W0	20A05
Minimal polynomial divides every annihilating polynomial	0VTAD25A3G	statement	W0	15A18
Order of a power	0VVPQNVM8S	statement	W0	20A05
Term test nth-term-test, divergence-test	0VVY4H92G2	statement	W1	40A05
Euler line	0VX0CPRQTZ	statement	W0	51M04
Gradient is orthogonal to level sets	0VXYV3NQQ1	statement	W0	26B12
Bézout's identity in a Euclidean domain	0VY3WPP9Y3	statement	W0	13F07
Compact closed unit ball implies finite dimension	0VZVV8VME5	statement	W0	46B50
Continuous functions on a closed bounded interval are uniformly continuous	0W0TZDRF9C	statement	W0	26A15
Euler's formula for planar graphs	0W1C598HMS	statement	W0	05C10
Line integral as an integral over the parameter interval parametric-formula-for-line-integrals	0W3W1VYWBP	statement	W0	26B12
Complete subspaces are closed	0W41XG4W60	statement	W0	54E50
Rank–nullity theorem dimension-theorem-for-linear-maps	0W4FSW1TVB	statement	W1	15A03, 15A04
Irrationality of e	0W4GQSG7B6	statement	W0	11J72
Law of total probability for an event and its complement	0W62TKMW7V	statement	W0	60A05
Epsilon-delta definition of continuity	0W8YHHGCJG	statement	W0	26A15
Chinese remainder theorem for rings	0W97J8QED7	statement	W0	13A15
Time translation of solutions of an autonomous system	0WA7ZR95V4	statement	W0	34A34
Trace of a linear map is the trace of its matrix	0WCPH5Z7FA	statement	W0	15A04, 15A15
R/M is a field iff M is maximal	0WD3SE7S1X	statement	W0	13A15
Euclid–Euler theorem	0WETJCKNRG	statement	W0	11A25
Sylvester's law of inertia	0WFED3K3DQ	statement	W1	15A63, 11E04
Newton's identities girard-newton-formulae	0WG2A3HE0S	statement	W1	05E05
A subspace of full dimension is the whole space	0WGAXEK99E	statement	W0	15A03
There is a natural number n with 1/n below any positive epsilon	0WH916TJNY	statement	W0	26A03
Taylor's theorem with the integral remainder	0WJGR81HBD	statement	W0	41A80
Dimension theorem for vector spaces invariance-of-dimension	0WK0Y8RH1M	statement	W0	15A03
Sylvester's criterion	0WKEF78PMV	statement	W1	15B57, 15A15
Cholesky decomposition	0WKG8CYY6A	statement	W1	15A23, 65F05
Product of exponentials exponential-of-a-sum	0WM7DJCM6G	statement	W0	33B10
Volume of a ball in R^3 volume-of-a-sphere	0WMDV48VSN	statement	W0	26B15
A prime is a Gaussian prime if and only if it is 3 modulo 4	0WMJSEFYFE	statement	W0	11R11
Hoeffding's inequality	0WPDNXGSSN	statement	W0	60E15
Moment-generating function of a sum of independent random variables	0WRZ170YEH	statement	W0	60E10
Extreme value theorem	0WS1A8E2P9	statement	W1	26A15
Cantor's theorem	0WTEMGYV2C	statement	W1	03E10
Gram–Schmidt vectors are orthogonal	0WXBGBTA3D	statement	W0	15A63, 65F25
A monotone function has countably many discontinuities froda-theorem	0WYTM4C9QG	statement	W0	26A48
Number of injections	0X0N833FF8	statement	W0	05A05
Hall's theorem for bipartite graphs	0X2GJPNPFN	statement	W0	05C70
Countable intersection of dense open sets is dense	0X2T63GFQQ	statement	W0	54E52
The exterior derivative squares to zero d-squared-is-zero	0X308R2DBE	statement	W0	58A10
Tietze extension theorem tietze-urysohn-extension-theorem	0X52TNMTCJ	statement	W1	54C20
Impossibility of squaring the circle	0X7CVDE3BG	statement	W0	12F05
Continuity of probability measures continuity-from-below, continuity-from-above	0X8HBKCSYB	statement	W0	60A10
Uniform limit theorem uniform-limit-of-continuous-functions-is-continuous	0X9XT05JVC	statement	W1	40A30, 26A15
Handshaking lemma	0XAP8WHNES	statement	W0	05C07
Wallis product	0XCYA4YERS	statement	W1	11Y60
Number of elements of each order in a cyclic group	0XCYGCCX8V	statement	W0	20K01
Monotonicity of the cumulative distribution function	0XD22PBMWA	statement	W0	60E05
Multinomial theorem	0XFC1VQYEK	statement	W1	05A10
Euler's partition theorem	0XFZ1BMF5Q	statement	W0	05A17
Decomposition of a permutation into transpositions	0XK6FECMW5	statement	W0	20B30
Poisson limit theorem law-of-rare-events, poisson-approximation-to-the-binomial	0XKTZRWTXX	statement	W1	60F05
Squeeze theorem sandwich-theorem	0XMF00T4XQ	statement	W1	40A05
Dini's theorem	0XRRYF1HPE	statement	W1	40A30
Eisenstein's lemma	0XSDBCP4RZ	statement	W0	11A15
The principal logarithm is holomorphic off the branch cut derivative-of-the-logarithm	0XVGJE7Q04	statement	W0	33B10
A root of an integer is an integer or irrational	0XWCKJZRYH	statement	W0	11J72
Second fundamental theorem of calculus	0XYAFCN0PT	statement	W0	26A42
De Morgan's laws in a Boolean algebra	0XYVDWGQX2	statement	W0	06E05
Absolutely convergent series converge	0Y123X48GA	statement	W0	40A05
Catalan recurrence	0Y1MG9R5VN	statement	W0	05A15
Gauss–Wantzel theorem	0Y34JMJNE9	statement	W0	12F05
The order modulo p divides p − 1	0Y4B7P0GS8	statement	W0	11A07
Trace of a product is symmetric	0Y4NF1DRKD	statement	W0	15A15
Brooks' theorem	0Y4TV2D5RQ	statement	W1	05C15
Fermat's Last Theorem flt	0Y5X3SDBCZ	statement	W1	11D41
Tail sum formula for expectation tail-sum-formula, layer-cake-formula-for-expectation	0Y6QNF1J49	statement	W0	60A05
Existence of an orthonormal basis	0Y85GYEGSF	statement	W0	15A63, 46C05
Distinct eigenvalues imply diagonalisable	0Y95Z7MT02	statement	W0	15A20
Binary trees are counted by Catalan numbers	0Y97E2DMB7	statement	W0	05C05
Comparability of cardinals trichotomy-of-cardinals	0YBHSJMN3J	statement	W0	03E10
Identity theorem uniqueness-theorem-for-holomorphic-functions	0YBVKMYX0W	statement	W0	30C15
Term-by-term integration	0YBY3VYX0K	statement	W0	40A30, 26A42
Matrix exponential as the solution of a linear system	0YC8JT513J	statement	W0	34A30, 15A16
Universal property of the tensor product	0YDRV01R8F	statement	W0	15A69
Continuity via open sets	0YF82GBTND	statement	W0	54E35
Sum of independent Poisson random variables	0YH1M56SBN	statement	W0	60E05
Irrationality of the square root of a prime	0YHFMXJJAZ	statement	W0	11J72
Hilbert's basis theorem	0YKA9J3XEE	statement	W1	13E05
Existence of nth roots of complex numbers	0YM6P6C206	statement	W0	12D99
Power series are holomorphic in the disc of convergence termwise-differentiation-of-power-series	0YMP521ZR5	statement	W0	30B10
Fundamental theorem of contour integration fundamental-theorem-for-complex-line-integrals	0YQ458D7PF	statement	W0	30E20
Intersecting chords theorem chord-theorem	0YQQYET8YQ	statement	W1	51M04
Pascal's rule	0YRG241HQQ	statement	W1	05A10
Closed balls are closed	0YS40B38JD	statement	W0	54E35
Homotopy invariance of line integrals of closed forms helmholtz-theorem-for-lamellar-fields	0YVVN6R715	statement	W0	26B20
Decomposition of a permutation into disjoint cycles	0YWDAZPRPQ	statement	W0	20B30
Quadratic reciprocity for the Jacobi symbol	0YY06KP3ZQ	statement	W0	11A15
Mercator series	0YZXNE3HFR	statement	W1	30B10, 33B10
Power series of complex cosine taylor-series-of-cosine	0Z1G2F8DGY	statement	W0	33B10
Diagonalisation of a quadratic form	0Z3FEWZ8HA	statement	W0	11E04, 15A63
Decomposition into generalised eigenspaces	0Z3GDY89T5	statement	W0	15A18, 15A21
A function with nonnegative second derivative is convex	0Z41C17TGP	statement	W0	26A51
Burnside's lemma orbit-counting-theorem, cauchy-frobenius-lemma	0Z47M1B2VS	statement	W1	20B05, 05E18
Determinant of the identity matrix	0Z4BWARC38	statement	W0	15A15
Local homeomorphism from the inverse function theorem invertible-derivative-implies-local-homeomorphism	0Z8CSYVHDJ	statement	W0	26B10
Countable union of countable sets is countable	0Z8FM54P86	statement	W0	03E10
Constant multiple rule	0Z9JB71BS0	statement	W0	26A24
Dimension of the space of linear maps	0Z9N1ER0W0	statement	W0	15A03, 15A04
Cauchy criterion for sequences	0ZA4AX4MW3	statement	W0	40A05
A complex number times its conjugate	0ZB7J071WQ	statement	W0	30A99
Gradient points in the direction of steepest ascent	0ZC78099PA	statement	W0	26B12
Orbits partition the set	0ZC7FYE0NZ	statement	W0	20B05
g to the order of the group is the identity power-of-the-group-order-is-identity	0ZEPNS9BXK	statement	W0	20D60
Universal property of the quotient space	0ZERJX6PH6	statement	W0	15A04
Transfinite induction well-founded-induction	0ZHQMQ2C1N	statement	W1	03E10
Canonical isomorphism with the double dual	0ZJM9D7NPS	statement	W0	15A04
Absorption law	0ZKZBJPG2J	statement	W0	06B05
Path-connected spaces are connected	0ZMT1GP4KM	statement	W0	54D05
First isomorphism theorem for rings	0ZMYX7GMH0	statement	W0	16D25
Determinant of a 2 by 2 matrix	0ZN2J42SK7	statement	W0	15A15
K(a) is isomorphic to K[x] modulo the minimal polynomial	0ZN39QDTP9	statement	W0	12F05
p-series test	0ZNSSK8ZK1	statement	W0	40A05
Matrix of the dual map is the transpose	0ZPB3180AY	statement	W0	15A04
Tower law for indices multiplicativity-of-the-index	0ZQJ7KEFQ5	statement	W0	20A05
The logarithm is strictly concave	0ZS54B9GJF	statement	W0	26A51
Intersection of subgroups is a subgroup	0ZTGMDNVTB	statement	W0	20A05
Uniqueness of limits	0ZXJ2455NJ	statement	W0	40A05
Second supplement to quadratic reciprocity	0ZXW95S44M	statement	W0	11A15
Determinant of a transpose	0ZZQ2E1MTE	statement	W0	15A15
Lagrange's theorem	3C53TD	statement	W0	20D60