Recent content by AnthonyAcc

  1. A

    Is Set B of Functions from Natural Numbers to {0,1} Countable?

    Let B={s|s is a function mapping the set of natural numbers to {0,1}}. Is B a countable set-that is, is it possible to find a function \Phi() mapping the set of natural numbers onto B-? I know that it has to do with infinite binary sequences, but the countability part confuses me. Can...
  2. A

    Proving (a+b)^n = ∑(n_μ)(a^μ)(b^(n-μ)) | a=1, b=-1 using Sequences Test

    A more fundamental question I have, I guess, is if I know that \sum^{\infty}_{\nu=0} (^{n}_{\nu}) a^{\nu} b^{n-\nu} = (a+b)^{n} then do I know that \sum^{n}_{\nu=0} (^{n}_{n-\nu}) a^{\nu} b^{n-\nu} = (a+b)^{n}? How does the changing of infinity to n and the \nu to n - \nu impact the series?
  3. A

    Proving (a+b)^n = ∑(n_μ)(a^μ)(b^(n-μ)) | a=1, b=-1 using Sequences Test

    Does this \sum^{\infty}_{\nu=0} (^{n}_{\nu}) imply \sum^{n}_{\nu=0} (^{n}_{\nu}) because it's for every n choose \nu so there can only be n many \nus?
  4. A

    Proving (a+b)^n = ∑(n_μ)(a^μ)(b^(n-μ)) | a=1, b=-1 using Sequences Test

    Show that (^{n}_{n}) - (^{n}_{n-1}) + (^{n}_{n-2}) - (^{n}_{n-3}) + ...(^{n}_{0}) = 0 (a+b)^{n} = \sum^{\infty}_{\nu=0} (^{n}_{\nu})a^{\nu}b^{n-\nu}a=1 b=-1 0 = (1+(-1))^{n} = \sum^{\infty}_{\nu=0}(^{n}_{\nu}) 1^{\nu}(-1)^{n-\nu} = \sum^{\infty}_{\nu=0}(^{n}_{\nu})(-1)^{n-\nu} = ...I don't...
  5. A

    Question about Sequences - sorry if this is in the wrong place.

    I'm taking an introductory class on analysis right now and I'm trying to get through the book that we are reading. I'm having difficulty understanding a park of it and was hoping someone could help me out. The part I'm reading about now is on null sequences: Here's an excerpt. I'm having...
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