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- Thread starter 1MileCrash
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- #2

phosgene

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Oops. It's just the contrapositive. Then no, it's not worthy of being a corollary.

- #3

fluidistic

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If it follows from the theorem 1.6 then why not? :) Not really funny to me.

- #4

1MileCrash

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Yes. Not all theorems work both ways like that.

Are you sure?

- #5

phosgene

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Are you sure?

I misread it, thought that the corollary was about dependance too.

- #6

1MileCrash

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I misread it, thought that the corollary was about dependance too.

Hah, I don't blame you. I had to do a double (or triple) take.

Though, interestingly enough, if the corollary was about dependence, then that would mean (S1 dependent) <=> (S2 dependent), which would mean that any subset or superset of any linearly dependent set would be linearly dependent. Which would mean that all subsets of a vector space would be linearly dependent, because all vector spaces must contain some linearly dependent subset (namely itself) (unless I'm just confusing myself here!)

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- #7

Office_Shredder

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- #8

1MileCrash

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_{2}the field of two elements, as a one dimensional vector space over itself.

I'm saying - if the corollary was talking about dependence, a consequence would be that any subset of a vector space is linearly dependent because the vector space itself is.

- #9

AlephZero

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- #10

FlexGunship

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Is this really worthy of being pointed out as a corollary??

Wait. Why? Because there's two extra commas in there?

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