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  "body": "\n## Summary\n\nThe characteristic of a field is the least positive number of copies of $1$ that add up to $0$.\nIt is $0$ when no such number exists.\nIt is the [[characteristic of the field as a ring|0F6ES3BRYP]], and for a field it is always $0$ or a prime number.\nIt decides the [[prime subfield|0TNS65QB87]], and many results of field theory depend on it.\nFor example, the map $a \\mapsto a^p$ is a ring homomorphism in characteristic $p$.\n\n## Explanations\n\n### L1 human\n\nStart at $0$ and add $1$ again and again.\nIn the rational or real numbers you never come back to $0$, so the characteristic is $0$.\nIn the field $\\F_7$ of integers modulo $7$, seven steps bring you back to $0$, so the characteristic is $7$.\nA field can never have characteristic $6$, because $2 \\cdot 3 = 0$ would make two nonzero elements multiply to $0$.\nThe [[definition|5ZXRZB41HE]] states this precisely.\n",
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