Comments on: Calculational proofs are usually direct http://www.joaoff.com/2008/02/11/direct-proofs/ Programming, Algorithms, and Mathematics Tue, 06 Jan 2009 15:39:53 +0000 http://wordpress.org/?v=2.6.1 By: jff http://www.joaoff.com/2008/02/11/direct-proofs/#comment-1306 jff Thu, 16 Oct 2008 21:34:19 +0000 http://www.joaoferreira.org/2008/02/11/direct-proofs/#comment-1306 Mike, The so-called Leibniz rule (also called 'substitution of equals by equals') states that, for all a, b, and function f: a = b => f.a = f.b . Hence, you can see the first step as a mutual implication where, in one direction, function f is taking the square root, and in the other direction, function f corresponds to squaring. Thanks for your comment! Mike,

The so-called Leibniz rule (also called ’substitution of equals by equals’) states that, for all a, b, and function f:

a = b => f.a = f.b .

Hence, you can see the first step as a mutual implication where, in one direction, function f is taking the square root, and in the other direction, function f corresponds to squaring.

Thanks for your comment!

]]> By: mike http://www.joaoff.com/2008/02/11/direct-proofs/#comment-1206 mike Mon, 15 Sep 2008 22:05:09 +0000 http://www.joaoferreira.org/2008/02/11/direct-proofs/#comment-1206 Hi. delicious!truly elegant! isn't the first equivalence actually an implication? m/n could be minus sqrt(2)... tks Hi.

delicious!truly elegant!

isn’t the first equivalence actually an implication? m/n could be minus sqrt(2)…

tks

]]> By: Erik http://www.joaoff.com/2008/02/11/direct-proofs/#comment-739 Erik Wed, 13 Feb 2008 21:14:15 +0000 http://www.joaoferreira.org/2008/02/11/direct-proofs/#comment-739 Thanks, I thought I was going mad. :) Thanks, I thought I was going mad. :)

]]> By: jff http://www.joaoff.com/2008/02/11/direct-proofs/#comment-737 jff Wed, 13 Feb 2008 20:37:57 +0000 http://www.joaoferreira.org/2008/02/11/direct-proofs/#comment-737 Dear Erik, of course I have. It was a typo, I'm sorry. It is corrected now. Thanks a lot! Dear Erik,

of course I have. It was a typo, I’m sorry. It is corrected now. Thanks a lot!

]]> By: Erik http://www.joaoff.com/2008/02/11/direct-proofs/#comment-735 Erik Wed, 13 Feb 2008 19:26:48 +0000 http://www.joaoferreira.org/2008/02/11/direct-proofs/#comment-735 Did you keep that sqrt on a little longer than necessary, or am I completely misunderstanding this proof? Did you keep that sqrt on a little longer than necessary, or am I completely misunderstanding this proof?

]]> By: jff http://www.joaoff.com/2008/02/11/direct-proofs/#comment-729 jff Mon, 11 Feb 2008 09:47:46 +0000 http://www.joaoferreira.org/2008/02/11/direct-proofs/#comment-729 Hmmm. I'm using a plugin called wp-latexrenderer. I have to investigate whether it works for comments. Hmmm. I’m using a plugin called wp-latexrenderer. I have to investigate whether it works for comments.

]]> By: Jonathan http://www.joaoff.com/2008/02/11/direct-proofs/#comment-727 Jonathan Mon, 11 Feb 2008 02:23:15 +0000 http://www.joaoferreira.org/2008/02/11/direct-proofs/#comment-727 nope nope

]]> By: Jonathan http://www.joaoff.com/2008/02/11/direct-proofs/#comment-726 Jonathan Mon, 11 Feb 2008 02:21:28 +0000 http://www.joaoferreira.org/2008/02/11/direct-proofs/#comment-726 by the way, comments on wordpress support the wordpress subset of LaTeX. But since there's no preview, if you goof, you have to ask the host to nicely fix things up. Let's try: $latex e^{i\pi}+1=0 $ by the way, comments on wordpress support the wordpress subset of LaTeX. But since there’s no preview, if you goof, you have to ask the host to nicely fix things up.

Let’s try:

$latex e^{i\pi}+1=0 $

]]> By: jff http://www.joaoff.com/2008/02/11/direct-proofs/#comment-725 jff Mon, 11 Feb 2008 00:25:03 +0000 http://www.joaoferreira.org/2008/02/11/direct-proofs/#comment-725 No problem :-) No problem :-)

]]> By: Jonathan http://www.joaoff.com/2008/02/11/direct-proofs/#comment-724 Jonathan Mon, 11 Feb 2008 00:18:41 +0000 http://www.joaoferreira.org/2008/02/11/direct-proofs/#comment-724 Slick. Thank you. Slick. Thank you.

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