- #1
Jarvis323
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- 986
Can [itex](0,1)\subset\mathbb{R}[/itex] be divided into an infinite set [itex]S[/itex] of non-empty disjoint subsets? It seams like any pair of points in different subsets of the partitioning must have a finite difference, and so there must be some smallest finite difference overall, [itex]d[/itex] where [itex]|S| \leq 1/d[/itex]. Can someone point me to the result of this question?