Math 2.0

object

Integers

Description

The integers are the numbers …,−3,−2,−1,0,1,2,3,…\dots, -3, -2, -1, 0, 1, 2, 3, \dots. We write Z\mathbb{Z} for the set of integers. The set Z\mathbb{Z} contains the natural numbers 0,1,2,…0, 1, 2, \dots and their negatives −1,−2,−3,…-1, -2, -3, \dots. With addition and multiplication, Z\mathbb{Z} is a commutative ring. Each integer aa has an additive inverse −a-a, thus subtraction is always possible in Z\mathbb{Z}. The integers have a total order that extends the order of N\mathbb{N}.

Remarks

The letter Z\mathbb{Z} comes from the German word "Zahlen", which means "numbers". One construction of the integers uses pairs of natural numbers. The rational numbers contain the integers as the fractions a/1a / 1.

Explanations

L1 human

The integers are the whole numbers with a sign: positive, negative or zero. You need them to answer questions such as 5−8=?5 - 8 = ?, which has no answer in the natural numbers. On a number line, the negative integers are to the left of 00.

What this node needs for W2
  • section Invariants: a table of the main invariants (0 of 1)
  • edge instance_of out (0 of 1)

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196 nodes use this node, directly or through other nodes.

Sources

  1. Web https://en.wikipedia.org/wiki/Integer, lead section
  2. Web https://en.wikipedia.org/wiki/Integer, Algebraic properties

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