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deepnorth
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« on: August 01, 2009, 11:18:26 AM »

http://www.mathcs.org/analysis/reals/cont/proofs/monodisc.html

From last paragraph.

"Since the sum of jumps must be smaller than f(b) - f(a), the set J(n) is finite for all n".

I can uderststand that the sum of jumps must be samller than f(b)-f(a), but why the Set J(n) is finite then?

Thanks.
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« Reply #1 on: August 03, 2009, 11:25:23 AM »

J(n) is the set of all jumps c where j(c) is greater than 1/n. If that set was infinite and you'd add them all up, you would add up infinitely many numbers bigger than 1/n. That would add up to infinity, which is impossible since the sum must be smaller than f(b) - f(a), a finite quantity.
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deepnorth
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« Reply #2 on: August 04, 2009, 10:42:36 AM »

Thanks, I see.
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