What is the set of $0$-combinations of $\{1,...,n\}$. The cardinality of this set is 1, so it can not be the empty set.
2026-04-02 18:42:37.1775155357
set of 0-combination of $\{1,...,n\}$
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$\varnothing$ has cardinality $0$, sure. However, $\{\varnothing\}$ has cardinality $1$, and that is the set containing all $0$-combinations. There is one $0$-combination, and that's the empty set.