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  "body": "\n## Statement\n\nEvery nonempty set of natural numbers has a least element.\nThat is, if $A \\subseteq \\mathbb{N}$ and $A \\neq \\emptyset$, then there is an $a$ in $A$ with $a \\le x$ for each $x$ in $A$.\n\n## Remarks\n\nThe least element is unique, because the [[order|0Y9H52BT03]] on $\\mathbb{N}$ is antisymmetric.\nThe principle follows from [[strong induction|0KMVFSHFGZ]], and conversely it implies the [[principle of mathematical induction|0ASJVEFA9J]].\nThe set of the integers does not have this property: the set of negative integers has no least element.\n\n## Explanations\n\n### L1 human\n\nIf some natural numbers have a property, then there is a smallest one with that property.\nFor example, among the natural numbers that are larger than $10$ and even, the smallest is $12$.\nProofs often use this: they take the smallest counterexample and show that it cannot exist.\n",
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