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  "body": "\n## Summary\n\nA lattice with a least element $0$ is atomic if every nonzero element lies above at least one [[atom|TTVCTW6TNC]].\nEvery finite lattice is atomic, and so is the lattice of all subsets of a set.\nThe notion separates lattices that are built from minimal pieces from atomless ones such as the interval $[0, 1]$.\nIt is weaker than being [[atomistic|99DVVV7BH2]], where every element is a join of atoms.\n\n## Explanations\n\n### L1 human\n\nIn an atomic lattice, whatever nonzero element one picks, one can always find a smallest possible nonzero piece inside it.\nIn the subsets of a set, a nonempty set contains a one-element subset.\nIn the positive integers ordered by divisibility, every number $n \u003e 1$ has a prime divisor.\nIn the interval $[0, 1]$ there is no smallest positive number, so it is not atomic.\n",
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