User:GFauxPas/Sandbox

Welcome to my sandbox, you are free to play here as long as you don't track sand onto the main wiki. --GFauxPas 09:28, 7 November 2011 (CST)


 * $u \ v \ \mathsf{u} \ \mathsf{v} \ \nu \ \upsilon$

Anyone else have a hard t--GFauxPas 14:32, 19 February 2012 (EST)ime distinguishing between $u$ and $v$? I would like it to look more like this, does it confuse anyone else? It seems PW doesn't have the upgreek package. --GFauxPas 07:49, 27 January 2012 (EST)


 * Nope. Multiple years of extensive TeX writing and reading have trained my eye. I agree that referenced $v$ looks more distinguished, but imagine it is hard to implement. --Lord_Farin 08:08, 27 January 2012 (EST)

Exponential Definitions
I am discussing the equivalence of the definitions of exponential here:

http://forums.xkcd.com/viewtopic.php?f=17&t=80256

For anyone who has been following my progress or lack thereof on exponent combination laws/log laws etc, feel free to look on. --GFauxPas 16:59, 6 February 2012 (EST)


 * Okay, it looks like $e^{xy} = e^xe^y$ was the hardest one to prove! I was expecting a walk uphill the whole way. Oh, my Linear Algebra book came in the mail, so I guess I'll work on vectors next. And one of these days I'll have to tie up loose ends with Tarski. --GFauxPas 16:57, 10 February 2012 (EST)

Cauchy Condensation Test
Krantz has a geometric proof for Cauchy Condensation Test that I think I can redo to fit PW standards. Does Geogebra have an option to graph a series/sequence? If not, I can just graph a dotted line and put dots on integer arguments, or something. --GFauxPas 14:32, 19 February 2012 (EST)
 * Don't know, haven't tried. Worth checking their help forum, I believe they have one or something similar. --prime mover 16:34, 19 February 2012 (EST)
 * I figured it out. Half of the proof is done, I think I can do the rest later today. --GFauxPas 16:50, 19 February 2012 (EST)
 * Please share your thoughts about how the geometric proof can be made more rigorous, PM? Should I do a geometric version and an analytic version of the proof at the same time, or...? I wasn't able to figure out how to do the proof analytically by grouping the partial sums appropriately, though I suspect I'm missing something obvious. --GFauxPas 00:10, 20 February 2012 (EST)
 * Take a look at how the technique is used in the proof that the series of reciprocals $\sum_\N \frac 1 n$ diverges. That proof is but an example of this one. Note, however, that there are neater ways of doing it that don't involve lost of visual groupings of things on the page. --prime mover 02:13, 20 February 2012 (EST)