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  "body": "\n## Description\n\nThe natural numbers are the numbers $0, 1, 2, 3, \\dots$ that count the elements of a finite set.\nWe write $\\mathbb{N} = \\{0, 1, 2, 3, \\dots\\}$ for the set of natural numbers.\nEach natural number $n$ has a next natural number $n + 1$, its successor.\nThe [[Peano axioms|0QFT7Z76N5]] describe $\\mathbb{N}$ with the number $0$ and the [[successor function|0AK9TGSNXY]].\nThe [[addition|0S13V32CPB]], the [[multiplication|06J5DE801P]] and the [[order|0HNATXFEV5]] of $\\mathbb{N}$ come from $0$ and the successor function.\n\n## Remarks\n\nSome authors start the natural numbers at $1$. They then write $\\mathbb{N}_0$ or $\\mathbb{Z}_{\\ge 0}$ for the set $\\{0, 1, 2, \\dots\\}$.\nEvery nonempty set of natural numbers has a least element. This is the [[well-ordering principle|01BX15HSRR]].\nThe [[integers|0C4JS9RF5M]] contain the natural numbers as the integers that are not negative.\n\n## Explanations\n\n### L1 human\n\nThe natural numbers are the numbers that you use to count: zero, one, two, three, and so on.\nThere is no largest natural number, because you can always add one more.\nAll the other number systems of this course, such as the integers and the real numbers, start from the natural numbers.\n",
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        "what": "section Invariants",
        "note": "a table of the main invariants",
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