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  "body": "\n## Summary\n\nThe order type of a totally ordered set is what it shares with every set that is [[order isomorphic|0Y74KN99A5]] to it.\nTwo ordered sets have the same order type exactly when there is an order isomorphism between them.\nStandard order types are $\\omega$ for the natural numbers, $\\eta$ for the rationals and $\\lambda$ for the reals.\nThe order types of well-ordered sets are the [[ordinal numbers|0RDJK7EQYY]].\n\n## Explanations\n\n### L1 human\n\nThe order type forgets what the elements are and keeps only how they are arranged.\nThe natural numbers $0, 1, 2, \\dots$ and the even numbers $0, 2, 4, \\dots$ are different sets, but both form one infinite line going up from a first element.\nSo they have the same order type, $\\omega$.\nThe integers are different in shape: they have no first element, so their order type is not $\\omega$.\n",
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