Show that if $X$ is an infinite set and $A$ is subset of the power set of $X$ containing only finite pairwise disjoint sets such that the union of all elements of $A$ is $X$, then cardinalities of $X$ and $A$ are equal.
2026-03-29 03:45:12.1774755912
Decomposition of an infinite set into pairwise disjoint subsets which exhaust set does not affect cardinality
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