I'm going to teach myself some math, and I'll be asking lots of potentially stupid questions. First up: Is there a difference between saying "a vector space" and "a set of vectors" ?
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I'm having trouble imagining what a set of vectors without rules is, but maybe this is somewhat semantic?
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Ah, okay I think I get it. So, when you just say "vector space" you mean a set of vectors with addition and multiplication allowed. But, when you say e.g. "inner product space" it's *a* vector space where you can also do inner products.
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Yeah, if you take a vector space and add a rule for doing inner products, it's an inner product space.
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Yeah, but an inner product space is still *a* vector space. That's what was throwing me. Thanks!
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Prove it.
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I could, but not in finite time.
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I dislike the word space on general principles.
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