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  "body": "\n## Definition\n\nA [[real number|08J2M1JYAG]] $x$ is irrational when $x$ is not a [[rational number|0NCJ5WXN6Z]].\nThat is, there are no integers $a$ and $b$ with $b \\neq 0$ and $x = a / b$.\nThe set of irrational numbers is $\\mathbb{R} \\setminus \\mathbb{Q}$.\n\n## Remarks\n\nThe number $\\sqrt{2}$ is [[irrational|0DZGSDHD92]]. The numbers $\\pi$ and $e$ are also irrational.\nThe decimal expansion of a real number is eventually periodic exactly when the number is rational. Thus the decimal expansion of an irrational number never repeats.\nThe set $\\mathbb{Q}$ is countable and $\\mathbb{R}$ is not, thus almost all real numbers are irrational.\n\n## Explanations\n\n### L1 human\n\nAn irrational number is a number on the number line that you cannot write as a fraction.\nThe length of the diagonal of a square with side $1$ is such a number: it is $\\sqrt{2} = 1.41421\\dots$.\n",
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