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Is $K[[x_1,x_2,\dots]]$ an $\mathfrak m$-adically complete ring?

I asked this question on Mathematics Stackexchange (link), but got no answer. Let $K$ be a field, let $x_1,x_2,\dots$ be indeterminates, and form the $K$-algebra $A:=K[[x_1,x_2,\dots]]$. Recall th …