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In mathematics, a sequence of functions { f n } {\displaystyle \{f_{n}\}} from a set S to a metric space M is said to be uniformly Cauchy if:
Another way of saying this is that d u → 0 {\displaystyle d_{u}\to 0} as m , n → ∞ {\displaystyle m,n\to \infty } , where the uniform distance d u {\displaystyle d_{u}} between two functions is defined by
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