Interesting problem (limits theory)
- From: precarion <precarion@xxxxxxxx>
- Date: Fri, 27 Oct 2006 13:03:49 EDT
Hello!
I was studing a quite interesting problem for a few days and I have some possible solutions but nothing I'm really certain of. I was wondering if any of you have some certain (it means - mathematicaly correct) ideas how to solve the following puzzle:
PROBLEM: Let f be a continuous real-valued function of a rational variable. Prove that there always exists an irrational number t in (R\Q), such that there is a real number (it means - finite) limit of f(x) as x tends to t.
We can also write it shortly as: Let f: Q->R, continuous. Show that there exists t in (R\Q), that: lim f(x) is real as (x -> t).
I would be very glad for your help, guys. And sorry for my poor English, but I'm not a native speaker.
Chris
precarion@xxxxxxxx
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