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## A Classic Result

Linear Algebra, Algebraic structures (Groups, Rings, Modules, etc), Galois theory, Homological Algebra
Tsakanikas Nickos
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### A Classic Result

Show that any vector space $\displaystyle V$ over a field $\displaystyle \mathbb{K}$ has a (Hamel) basis.

Furthermore, show that any two bases of $\displaystyle V$ have the same cardinality.

Additionally, show that if $\displaystyle X$ is an infinite dimensional Banach space, then every Hamel basis of $\displaystyle X$ is uncountable.