If $B\subset A$, is it true that $Card(A)\backslash Card(B)$ is idempotent to $A\backslash B$ ? It seems to be true though I do not know how to prove it.
2026-04-03 21:42:06.1775252526
Cardinality of the set difference.
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No, this is not necessarily true. For instance, let $A=\mathbb{Z}$ and $B=\mathbb{N}$. Then $A\setminus B$ is infinite, but $A$ and $B$ have the same cardinality so the set difference between their cardinalities is empty.