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  "body": "\n## Summary\n\nOrdinal arithmetic is the addition, multiplication and exponentiation of [[ordinal numbers|0YSCSX5YZC]].\nThe operations extend those of the natural numbers to transfinite ordinals, and they are [[defined|2C7MBG93AZ]] by transfinite recursion or by order types of well-ordered sets.\nThey are not commutative, and they are the language of ordinal notations, such as the [[Cantor normal form|6GD30FGYDZ]].\n\n## Explanations\n\n### L1 human\n\nThink of an ordinal as a queue of positions.\nAdding $\\alpha + \\beta$ means placing the queue $\\beta$ after the queue $\\alpha$.\nMultiplying $\\alpha \\cdot \\beta$ means taking $\\beta$ copies of $\\alpha$, one after the other.\nOrder matters: $1 + \\omega$ puts one extra point before an infinite queue, which gives again a queue of type $\\omega$.\nBut $\\omega + 1$ puts a point after all the natural numbers, which is a longer queue.\nSo $1 + \\omega = \\omega$ while $\\omega + 1 \u003e \\omega$.\n",
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