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  "body": "\n## Definition\n\nLet $\\mathbb{N}$ be the set of [[natural numbers|0MWKJ44V5A]] and let $S$ be the [[successor function|0832XVR512]].\nAddition is the function $+ \\colon \\mathbb{N} \\times \\mathbb{N} \\to \\mathbb{N}$, $(a, b) \\mapsto a + b$, with these two properties for all $a$ and $b$ in $\\mathbb{N}$:\n$$a + 0 = a, \\qquad a + S(b) = S(a + b).$$\n\n## Remarks\n\nFor each $a$, these equations are a [[definition by recursion|0DSHAVH45F]] on $b$. Thus exactly one such function exists.\nWith $1 = S(0)$, the second equation gives $a + 1 = S(a)$.\nFor example, $2 + 2 = S(2 + 1) = S(S(2 + 0)) = S(S(2)) = 4$.\n\n## Explanations\n\n### L1 human\n\nTo add $b$ to $a$, you start at $a$ and count up $b$ steps.\nThe definition says this in two rules: adding $0$ changes nothing, and adding one more step gives the next number.\n",
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