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  "body": "\n## Summary\n\nLet $M$ be a module over a [[commutative ring|0310REJJY8]] $R$, and let $I$ be an [[ideal|096Z9MP2ME]] of $R$.\nIn the $I$-adic topology on $M$, the submodules $I^n M$ form a base of neighbourhoods of $0$.\nTwo elements are close when their difference lies in a high power of $I$.\nIt is the topology behind the [[completion of a ring|KBN13NPYJQ]], and the $p$-adic topology on $\\Z$ is the main example.\n\n## Explanations\n\n### L1 human\n\nIn this topology an element is small when it is divisible by a high power of $I$.\nFor the integers and $I = (2)$, the number $2^{10}$ is very small and $1024 + 3$ is very close to $3$.\nThe powers $2, 4, 8, 16, \\dots$ tend to $0$, which never happens for the usual distance on the real line.\nThe [[definition|MJDV3PFBRT]] makes this precise.\n",
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