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  "body": "\n## Example\n\nFix a signature $\\sigma$.\nThe *trivial variety* of signature $\\sigma$ is the class of all algebras of signature $\\sigma$ that satisfy the [[identity|PKD440G2XW]] $x = y$.\nAn algebra satisfies $x = y$ exactly when any two of its elements are equal, so the trivial variety consists of the one-element algebras.\nIt is a [[variety|AJNZJD8442]] because it is defined by an identity.\nThe check by closure is also direct.\nA subalgebra or a homomorphic image of a one-element algebra has one element.\nA direct product of one-element algebras has one element, and the empty product is a one-element algebra too.\n\n## Remarks\n\nEvery variety of signature $\\sigma$ contains all one-element algebras of signature $\\sigma$, since a one-element algebra satisfies every identity.\nSo the trivial variety is the least element of the [[lattice of subvarieties|GJAYCVYZYF]] of any variety.\nIts equational theory is the largest one: it contains every identity of signature $\\sigma$.\n\n## Explanations\n\n### L1 human\n\nThe trivial variety is the smallest possible variety: it only has algebras with one element.\nIn such an algebra, every operation has only one possible value, so there is nothing to compute.\nEvery other variety contains it.\n",
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