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Math Help - Calculus proof methods...

  1. #1
    Super Member Deadstar's Avatar
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    Oct 2007
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    Calculus proof methods...

    Maybe in the wrong forum...

    I was just curious as to how everyone here approaches rigorous calculus proofs, I'm thinking more specifically about convergence and related topics. I find that no matter how many examples I do I always find myself lost on the next Q. Here's an example...

    Let (a_n) and (b_n) be two sequences of real numbers such that a_n -> 0 and (b_n) is bounded. Show that a_n b_n -> 0.

    My first thought was that since b_n is bounded then there must exist a k such that |b_n| < k, and so |a_n b_n| -> 0k = 0..? But the proof was...

    => We have M such that |b_n| \le M for all n. Let \epsilon > 0. Then we can find m such that n>m implies |a_n| < \frac{\epsilon}{M}. Then for n>m we have |a_n b_n| \le M|a_n| < M\frac{\epsilon}{M} = \epsilon as required.

    Is there a way to learn these methods other than doing lots of examples which, i feel aren't really helping me... About to start subsequential limits and every Q scares the hell out o me.

    So basically, strange post i know but does anyone have any methods they use for proofs?
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  2. #2
    Member
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    Sep 2008
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    I hope someone replies to this post so bump. I'm have the same reasoning as you and could use some help in understanding all this.
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