Let $I$ be an ideal of a ring $R$. The $I$-adic completion of $R$ is defined as the inverse limit of the rings $R/I^n$, that is, the subring of $\prod\limits_{i=0}^\infty R/I^n$ that consists of sequences $(a_i)$ such that $a_m \equiv a_k \mod I^k$ for all $m > k$.
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