- #26

- 3,003

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So. Back to my annoying questions. (this is a continuation of post #20)

If I am given a set S={1,2,3,4,5} and I am told that it is a vector space, then something is flawed here since the sum of many of those elements are not themselves in the set. So what I have I done to cause this conflict.

Does a Vector space have to be infinite to rectify this?

i.e, since from S we could take 5+5=10, then S would have to include 10 to be a vector space...but then the cycle starts again since for example 5+10=15.

If I am given a set S={1,2,3,4,5} and I am told that it is a vector space, then something is flawed here since the sum of many of those elements are not themselves in the set. So what I have I done to cause this conflict.

Does a Vector space have to be infinite to rectify this?

i.e, since from S we could take 5+5=10, then S would have to include 10 to be a vector space...but then the cycle starts again since for example 5+10=15.

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