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  "body": "\n## Summary\n\nIn a [[partially ordered set|0QV2JS9RJ3]] with a [[least element|0AANKKNHS4]] $0$, an atom is an element just above $0$.\nIt is above $0$, and nothing lies strictly between $0$ and it.\nAtoms are the minimal nonzero elements.\nIn the lattice of subsets of a set they are the one-element subsets, which is the origin of the name.\nAtoms are used to define atomic and atomistic lattices and to describe Boolean algebras.\n\n## Explanations\n\n### L1 human\n\nAn atom is a smallest piece that is not nothing.\nIn the subsets of $\\set{1, 2, 3}$, the empty set is nothing, and the atoms are $\\set{1}$, $\\set{2}$ and $\\set{3}$.\nIn the positive integers ordered by divisibility, the bottom is $1$ and the atoms are the prime numbers, since the only divisors of a prime $p$ are $1$ and $p$.\nSome orders have no atoms at all: in the interval $[0, 1]$, between $0$ and any $a \u003e 0$ lies $a / 2$.\n",
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    "tag": "TTVCTW6TNC"
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  "link": "https://tamnd.github.io/math2/node/TTVCTW6TNC/",
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  "markdown": "https://tamnd.github.io/math2/node/TTVCTW6TNC.md",
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  "name": "Atom",
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  "source": "https://github.com/tamnd/math2/blob/main/nodes/TTV/TTVCTW6TNC.md",
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  "tag": "TTVCTW6TNC",
  "uri": "m2://TTVCTW6TNC",
  "url": "https://tamnd.github.io/math2/wiki/atom/",
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