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  "body": "\n## Summary\n\nThe term algebra over a set of variables is the algebra whose elements are the [[terms|6D3WA7N2W4]] themselves.\nIts operations build bigger terms from smaller ones.\nIt is the absolutely free algebra on the variables.\nEvery map from the variables into an algebra of the same signature extends to a unique homomorphism, given by [[term evaluation|DH30WTA26T]].\nAll free algebras of varieties are quotients of term algebras, and the syntax of equational logic lives in it.\n\n## Explanations\n\n### L1 human\n\nIn a term algebra, nothing is simplified.\nWith one binary symbol $\\cdot$ and variables $x, y$, the elements are expressions such as $x$, $x \\cdot y$, $(x \\cdot y) \\cdot x$ and $x \\cdot (y \\cdot x)$.\nTwo expressions are equal only if they are written the same way, so $(x \\cdot y) \\cdot x$ and $x \\cdot (y \\cdot x)$ are different elements.\nThe operation simply puts two expressions side by side with the symbol between them.\n",
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