Rigorous proof of Q39 (infinite triangle question)

Forum for the GRE subject test in mathematics.
yoyostein
Posts: 36
Joined: Tue Feb 28, 2012 12:14 am

Rigorous proof of Q39 (infinite triangle question)

Postby yoyostein » Thu Mar 15, 2012 1:55 am

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.

blitzer6266
Posts: 61
Joined: Sun Apr 04, 2010 1:08 pm

Re: Rigorous proof of Q39 (infinite triangle question)

Postby blitzer6266 » Sat Mar 17, 2012 4:12 am

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.




Return to “Mathematics GRE Forum: The GRE Subject Test in Mathematics”



Who is online

Users browsing this forum: Bing [Bot], itosformula and 4 guests