Given two Hilbert spaces.
Clearly, equal Hilbert dimension implies equal Hamel dimension.
(Similarly, equal Hamel dimension implies equal cardinality.)
But what about the converse?
(Sadly, I couldn't find something on MSE.)
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José Carlos Santos
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I think the first answer to http://math.stackexchange.com/questions/141535/cardinality-of-a-hamel-basis-of-ell-1-mathbbr has the answer, if I am interpreting correctly. – Disintegrating By Parts Sep 03 '16 at 01:58