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)