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1  Computer Science / Robotics Forum / Self-Registration disabled because of Spam on: March 17, 2010, 06:37:49 PM
Self-registration for this board has been disabled; we have had too many registrations by spammers who posted questionable, irrelevant, and frequently offensive content. If you are not currently a member and would like to post a question, please do so via email.

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2  Computer Science / Java Forum / Self-Registration disabled because of Spam on: March 17, 2010, 06:37:10 PM
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3  Mathematics / Statistics Forum / Self-Registration disabled because of Spam on: March 17, 2010, 06:35:46 PM
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4  Mathematics / Complex Analysis Forum / Self-Registration disabled because of Spam on: March 17, 2010, 06:35:18 PM
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5  Mathematics / Real Analysis Forum / Self-Registration disabled because of Spam on: March 17, 2010, 06:34:45 PM
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6  General Category / General Discussion / Self-Registration disabled because of Spam on: March 17, 2010, 06:32:45 PM
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7  Mathematics / Real Analysis Forum / Re: An elusive sequence... on: February 21, 2010, 07:05:26 PM
Check http://www.mathcs.org/analysis/reals/infinity/countble.html for sets and sequences that are countable yet contain intuitively "a lot" of numbers.
8  Mathematics / Real Analysis Forum / Re: An elusive sequence... on: February 21, 2010, 12:08:03 PM
Perhaps it is not that bad. A sequence just means it must be a countable set so you are looking for a countable set that is 'dense', or in simpler terms kind of 'everywhere'. That might be a well known set, and since it is countable you can think of it as a sequence. If you find that set/sequence the rest might might not be too bad. Good luck!
9  Mathematics / Real Analysis Forum / Re: how to prove the absolute value of any continuous function is continuous. on: November 09, 2009, 09:41:44 AM
I would go about it using the definition of absolute value, together with the fact that f(x) is continuous. Something like this:

Recall |f(x)| = f(x) if f(x) >= 0 or -f(x) if f(x) < 0

By assumption f(x) is continuous at c, i.e. |f(x) - f(c)| < epsi if |x - c| < delta

You need to show that | |f(x)| - |f(c)| | < epsi if |x - c| < delta

Now try three cases:

(1) f(c) > 0, which also implies that f(x) > 0 if x and c are close enough (why?) ... (use def of |f(x)|)
(2) f(c) < 0, which also implies that f(x) < 0 if x and c are close enough (why?) ... (use def of |f(x)| again but factor out a minus sign ...)
(3) f(c) = 0, which follows right away from f being continuous

Hope it helps, best of luck.
10  Mathematics / Real Analysis Forum / Re: Do you want minor edits on: October 30, 2009, 03:38:43 PM
It depends. If it's a minor typo, it will take until the next bigger problem s discovered. If it's a typo that makes the proof or statement non-comprehensible, I'll fix it quickly. If it's bigger problem, it might again take longer to fix, as more than one thing might depend on the one change. If you need something fixed urgently, let me know and I'll try my best.
11  Mathematics / Real Analysis Forum / Re: PROVE on: October 30, 2009, 03:32:05 PM
You should find the answer in the Real Analysis chapter 2.4 http://www.mathcs.org/analysis/reals/infinity/reals.html
12  Computer Science / Java Forum / Re: Problem with activating account on: October 20, 2009, 10:06:35 AM
Since you were able to post, it seems your registration worked out after all. Let me know if you still have problems.
13  Mathematics / Real Analysis Forum / Re: Proposition 6.4.1: Continuity and Topology on: August 06, 2009, 03:11:59 AM
Well, thank YOU for helping to fix typos and more serious mistakes - please keep it up!
14  Mathematics / Real Analysis Forum / Re: Proposition 6.4.1: Continuity and Topology on: August 05, 2009, 02:06:57 PM
Right, I think it should say: "take any x_0 in D ...", and perhaps somehow the fact that D is open should matter, too, don't you think?
15  Mathematics / Real Analysis Forum / Re: A question on: August 03, 2009, 11:34:59 AM
Saying "you can easily check" does not guaranty that it is right - you are correct, the limit (from the left and from the right) is of course 6, not 4, and on top of it the picture is wrong, too. I'll fix it as soon as I have a chance, thanks for pointing it out. - (fixed!)
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