## Strange vector spaces

What are some of the strangest vector spaces you know? I don't know many, but I like defining V over R as 1 tuples. Defining vector addition as field multiplication and scalar multiplication as field exponentiation. That one's always cool. Have any cool vector spaces? Maybe ones not over R but over maybe more exotic fields?
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 Quote by WannabeNewton R over Q is infinite dimensional. That's kinda cool I guess :p.
Never thought of that, but that's true. That's awesome.

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## Strange vector spaces

I also liked it when I realised that some sets functions are a vector space and you can basically think of them as n-tuples (for $n = 2^{\aleph_0}$). Was the first time I saw that vector spaces don't need to consist of actual points in $\mathbb{R}^k$.

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