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  "body": "\n## Summary\n\nIn universal algebra, an identity is an equation between two [[terms|6D3WA7N2W4]] that is required to hold for every value of the variables.\nLaws such as associativity $x(yz) \\approx (xy)z$ and commutativity $xy \\approx yx$ are identities.\nClasses of algebras defined by identities are called varieties, and much of universal algebra studies which identities hold in which algebras.\n\n## Explanations\n\n### L1 human\n\nAn identity is a rule that holds no matter which elements you plug in.\nIn the integers, $x + y \\approx y + x$ is an identity: swap any two numbers in a sum and the result does not change.\nThe equation $x + x \\approx x$ is not an identity of the integers, since it fails for $x = 1$, even though it holds for $x = 0$.\nIn a Boolean algebra, however, $x \\vee x \\approx x$ is an identity.\n",
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