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Rigorous proof of Q39 (infinite triangle question)

Posted: Thu Mar 15, 2012 1:55 am
by yoyostein
Hi,

For this question, the answer claims that the limit of (s-r) is a positive number less than 1.

I can understand the part about less than one, since the triangle inequality gives r+1>s => 1>s-r.

However, how do we prove that it must be positive (>0) and cannot be zero?

Thanks a lot for help.

Re: Rigorous proof of Q39 (infinite triangle question)

Posted: Sat Mar 17, 2012 4:12 am
by blitzer6266
Project s down to the "x-axis". Then |proj_r(s)| <= s, but proj_r(s) - r = some constant > 0 for all r. Thus lim s -r > lim proj_r(s) - r > 0.