How to determine whether a infinite set of functions is dependent or independent?
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Step-by-step explanation:
Putting t=0 in (1) we see that c0=0. (Why? I don't see this, and it's my biggest stumbling block in the proof.) Now divide by t in (1) and put t=0 again to find c1=0. (So, I'm confused as to what is meant by t in the proof. Is it all t? Also, why can we divide by t? Didn't we just say that t=0? Are there supposed to be subscripts?). Rinse and Repeat for the rest of the ck.
I have one last question. The sum in (1) is finite. How does this prove that an infinite set is independent. Doesn't this show that only n μi's are independent; rather than all μk for k=0,1,… are independent.
Update 1: Why t are we concerning ourselves with the case when t=0?
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