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  "body": "\n## Description\n\nThe integers are the numbers $\\dots, -3, -2, -1, 0, 1, 2, 3, \\dots$.\nWe write $\\mathbb{Z}$ for the set of integers.\nThe set $\\mathbb{Z}$ contains the [[natural numbers|0MWKJ44V5A]] $0, 1, 2, \\dots$ and their negatives $-1, -2, -3, \\dots$.\nWith addition and multiplication, $\\mathbb{Z}$ is a [[commutative ring|0BXA4Q0JHW]]. Each integer $a$ has an additive inverse $-a$, thus subtraction is always possible in $\\mathbb{Z}$.\nThe integers have a [[total order|0F6FM9Y4Y6]] that extends the order of $\\mathbb{N}$.\n\n## Remarks\n\nThe letter $\\mathbb{Z}$ comes from the German word \"Zahlen\", which means \"numbers\".\nOne [[construction of the integers|0NS58JP68E]] uses pairs of natural numbers.\nThe [[rational numbers|0NCJ5WXN6Z]] contain the integers as the fractions $a / 1$.\n\n## Explanations\n\n### L1 human\n\nThe integers are the whole numbers with a sign: positive, negative or zero.\nYou need them to answer questions such as $5 - 8 = ?$, which has no answer in the natural numbers.\nOn a number line, the negative integers are to the left of $0$.\n",
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