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  "body": "\n## Definition\n\nA complex number is transcendental if it is not an [[algebraic number|0MB4TGMXG6]].\nThat is, it is not a root of any nonzero polynomial with rational coefficients.\n\n## Remarks\n\nThe numbers $e$ and $\\pi$ are transcendental, by the [[Lindemann–Weierstrass theorem|0JNCBFMPXR]].\nEach [[Liouville number|0J1R5NP36S]] is transcendental, by [[Liouville's theorem|0N3WFZEFPM]].\nThe algebraic numbers are countable, so almost all real numbers are transcendental.\nJoseph Liouville first proved that transcendental numbers exist, in 1844.\n\n## Explanations\n\n### L1 human\n\nA transcendental number solves no polynomial equation with integer coefficients.\nIt is usually hard to prove that a given number is transcendental, even though most numbers are.\n",
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