Comments on: 245A: Problem solving strategies

By: Clark Zinzow

Clark Zinzow — Thu, 28 Feb 2013 08:36:29 +0000

Although I am not fluent in MathJax, I do not think that your correction is correct. His use of the normal subset is correct, since it is stating that E is a proper subset of F or E is equal to F, and vice versa, allowing for the potential of equality. Whereas your notation (assuming that “\subseteq” is referring to the subset symbol with a horizontal line underneath it) refers to a proper subset exclusively, therefore not allowing for the potential of equality since E being a proper subset of F implies that there exists some element in F such that the same element is not in E, and vice versa.

Please let me know if I misunderstood! I know that some mathematicians occasionally use the proper subset symbol to mean “a subset of or equal to”, much to the chagrin of those raised by baby and/or adolescent Rudin (the text, not the man).

By: Parth Kohli

Parth Kohli — Fri, 28 Dec 2012 20:54:29 +0000

Sorry, I do not know how to render MathJax here.

By: Parth Kohli

Parth Kohli — Fri, 28 Dec 2012 20:53:18 +0000

Prof. Terrence, please let me point out a mistake.

“In a similar spirit, to show that two sets E and F are equal, try proving that and $E \subset B$ and $B \subset E$.”

I believe that it’d be the following instead:

“In a similar spirit, to show that two sets E and F are equal, try proving that $E \subseteq B$ and $B \subseteq E$.

Regards.

By: Some outside help… | Analysis Quals

Some outside help… | Analysis Quals — Mon, 02 May 2011 05:01:39 +0000

[...] Posted on May 1, 2011 by eekelly2388 Jeremy just sent me this link to Terry Tao’s blog about common problem solving strategies for analysis. I can especially relate to number 9, try simpler cases first. Also, number 15 is a great trick; [...]

By: Anonymous

Anonymous — Wed, 05 Jan 2011 13:18:34 +0000

When you call “Give yourself an epsilon of room” a standard trick, do you mean it is the ONLY way to handle such kind of problems? I was wondering whether it is right to say that most of the problems in analysis is about dealing with “epsilon”. (maybe according to Halmos’s experiences?)

By: science and math

science and math — Mon, 03 Jan 2011 05:09:06 +0000

Nice tips.
Thanks for sharing the tips with us.

By: Universality and Characteristic Polynomials « Graduated Understanding

Universality and Characteristic Polynomials « Graduated Understanding — Sat, 11 Dec 2010 01:23:15 +0000

[...] you feel are irrelevant to the current problem. Terry tao discusses a similar trick in analysis (trick 10) in his “problem solving strategies,” [...]

By: Terence Tao

Terence Tao — Thu, 18 Nov 2010 18:12:46 +0000

The issue is the reverse implication. 0: X \leq Y+\epsilon' title='\exists \epsilon > 0: X \leq Y+\epsilon' class='latex' /> does not imply , but 0: X \leq Y+\epsilon' title='\forall \epsilon > 0: X \leq Y+\epsilon' class='latex' /> does.

By: Anonymous

Anonymous — Thu, 18 Nov 2010 18:09:57 +0000

Could you please explain? (Sorry to bother with such a basic question but I am not a mathematician) As I see it if some quantity then .
Thanks.

By: Anonymous

Anonymous — Thu, 18 Nov 2010 11:46:33 +0000

In the first paragraph fir trick 2 shouldn’t it be for ‘some’ instead of for ‘any’ ? [No - T.]