Let $(X, d)$ be a metric space, what is the negation of the definition that $(X, d)$ is complete?
I know a metric space is complete if every Cauchy sequence is convergent. I got really confused now.
2026-03-28 11:34:13.1774697653
What is the negation of the definition that a metric space is complete?
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$(X,d)$ is not complete $ \iff$ there is a Cauchy sequence $(x_n)$ in $X$ and no $x \in X$ such that $d(x_n,x) \to 0$ as $n \to \infty.$