>Thomas: > >>You haven't used or mentioned any coefficient yet. Here >>is a way of phrasing it: >> >>(* continued): "... given any coefficient c1,c2,...,cn ..." (you have >>to give those things a name!) "... c1*v1+c2*v2+...+cn*vn = 0 ..." >>(that's the "that") "... implies c1=c2=...=cn=0" >> >>So, now you have a formal definition! > >But, that's exactly what I said, even if my wording made it a little confusing.
No, you said something different and - frankly - incoherent. It is not verifyable and falsifiable. And one phrasing was even wrong: "...such that if they all equal the zero vector..."
> I knew that this was the definition, so you can't say I don't know the >definition of "independence".
But I can't say that you know, either.
>I may not know how to phrase it exactly, but I >know what an "independent set" is. Why should such a precise definition be >needed for computation? (I can understand for proofs, but I gotta work out >computational mistakes first.)
You can prove that by solving practical problems, that's a different story.