Suppose $F$ is a field and $J$ an infinite set. Is it then true that $\mathrm{card} \ J<\mathrm{card} \ F^J$? ($F^J$ the set of maps $J\rightarrow F$) I know that $\leqslant $, but is it true and why that we have $<$?
2026-03-29 07:21:04.1774768864
Cardinality question on vector spaces
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It follows from Cantor's theorem.