phosgene said:Yes. Not all theorems work both ways like that.
1MileCrash said:Are you sure?![]()
phosgene said:I misread it, thought that the corollary was about dependence too.![]()
Office_Shredder said:That's true, but not for the reason that you seem to be thinking. Every vector space contains 0, and therefore is a linearly dependent set, but if you remove that point you could have a linearly independent set. For example (and probably the only example), F2 the field of two elements, as a one dimensional vector space over itself.
1MileCrash said:Is this really worthy of being pointed out as a corollary??