Good evening,
I want to show that all bases of a vector space have the same cardinality, and it needs the following equality : Let $\aleph_0$ be the cardinality of $\mathbb{N}$ and $X$ an infinite set, then $\aleph_0 \operatorname{card}(X) = \operatorname{card}(X).$
Does anyone know where there is a proof for this equality?
Thanks in advance,
Duc Anh