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this is what you're talking about? http://puu.sh/iMtN8/0b7006bf62.png

i am sure it is in a textbook
that is why they cost like $250

I have the book. I'm having difficulty following the proof

and why is it written differently from the way it was written in theorem?

i'm still not getting it :/

this uniqueness part looks unnecessarily complicated

and recall that if \(f:A\to B\) is an injection then \(|A|\le |B|\)

pigeonhole principle

ok, here is the stupid question. Why is b_k(1) = 1? XD and also b_k(k^n) = 1

but that's enough for us since we're only using \(b^k(k^p)\) as a lower-bound

ah yeah because 1 <= b_k(k^n) <=1 thus b_k(k^n) = 1

oops, \(b_k(k^n)\) as a lower bound* and yes exactly, it gets sandwiched between

Yeah I know

by 'works' i mean gives unique representations

Sure this is just one instance, we don't have to have the basis following any pattern at all.

i think there are some conditions you need to prove as well to ensure that's enough @ganeshie8

like \(a_0,~~a'_0\ne 0\) and \(a_{s-t},~~a'_{s-t}\ne 0\) ?

nah, but I think it's trivial anyways