Comments for João Ferreira http://www.joaoff.com Programming, Algorithms, and Mathematics Sat, 22 Nov 2008 07:58:05 +0000 http://wordpress.org/?v=2.6.1 Comment on Calculational proofs are usually direct 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!

]]> Comment on A square grid path problem by jff http://www.joaoff.com/2008/01/20/a-square-grid-path-problem/#comment-1305 jff Thu, 16 Oct 2008 21:25:03 +0000 http://www.joaoferreira.org/2008/01/20/a-square-grid-path-problem/#comment-1305 Amanda, just replace n by 8 in the first formula and you get the desired result :) Amanda,

just replace n by 8 in the first formula and you get the desired result :)

]]> Comment on A square grid path problem by amanda http://www.joaoff.com/2008/01/20/a-square-grid-path-problem/#comment-1300 amanda Thu, 16 Oct 2008 00:13:13 +0000 http://www.joaoferreira.org/2008/01/20/a-square-grid-path-problem/#comment-1300 hey! how many solutions would be in a 8X8? =D hey!
how many solutions would be in a 8X8?
=D

]]> Comment on On Programming and Mathematical Methodology — Part II by jff http://www.joaoff.com/2007/01/15/on-programming-and-mathematical-methodology-part-ii/#comment-1279 jff Sat, 11 Oct 2008 11:28:04 +0000 http://www.joaoferreira.org/2007/01/15/on-programming-and-mathematical-methodology-part-ii/#comment-1279 Thanks Ronel. I am not planning to write a part III. Instead, I'll try to convey other ideas using particular examples. Thanks Ronel. I am not planning to write a part III. Instead, I’ll try to convey other ideas using particular examples.

]]> Comment on On Programming and Mathematical Methodology — Part II by ronel banan http://www.joaoff.com/2007/01/15/on-programming-and-mathematical-methodology-part-ii/#comment-1276 ronel banan Sat, 11 Oct 2008 01:02:25 +0000 http://www.joaoferreira.org/2007/01/15/on-programming-and-mathematical-methodology-part-ii/#comment-1276 awts!!! very nice article.. wish that part 3 will come awts!!! very nice article.. wish that part 3 will come

]]> Comment on Calculational proofs are usually direct 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

]]> Comment on A square grid path problem by Nektra Advanced Computing Blog :: Google Treasure Hunt puzzles are too easy? http://www.joaoff.com/2008/01/20/a-square-grid-path-problem/#comment-894 Nektra Advanced Computing Blog :: Google Treasure Hunt puzzles are too easy? Fri, 23 May 2008 18:40:32 +0000 http://www.joaoferreira.org/2008/01/20/a-square-grid-path-problem/#comment-894 [...] gets solved just searching in Google for “grid path right down” from there you will get the equation that you must run on any language that has Big Integer implementations, since involves the [...] [...] gets solved just searching in Google for “grid path right down” from there you will get the equation that you must run on any language that has Big Integer implementations, since involves the [...]

]]> Comment on A square grid path problem by jff http://www.joaoff.com/2008/01/20/a-square-grid-path-problem/#comment-893 jff Sun, 18 May 2008 01:06:09 +0000 http://www.joaoferreira.org/2008/01/20/a-square-grid-path-problem/#comment-893 Dr. Goulu: no problem! Good luck with Google's challenge. Dr. Goulu: no problem! Good luck with Google’s challenge.

]]> Comment on A square grid path problem by Recrutement et Casse-Tête « Dr. Goulu http://www.joaoff.com/2008/01/20/a-square-grid-path-problem/#comment-892 Recrutement et Casse-Tête « Dr. Goulu Sat, 17 May 2008 22:06:43 +0000 http://www.joaoferreira.org/2008/01/20/a-square-grid-path-problem/#comment-892 [...] pour un damier de 56×32 cases (le nombre change pour chaque participant) et dans ce cas, la réponse est 232059241971866600926656. Ca suppose donc déjà de disposer d’une bonne calculatrice [...] [...] pour un damier de 56×32 cases (le nombre change pour chaque participant) et dans ce cas, la réponse est 232059241971866600926656. Ca suppose donc déjà de disposer d’une bonne calculatrice [...]

]]> Comment on A square grid path problem by Dr. Goulu http://www.joaoff.com/2008/01/20/a-square-grid-path-problem/#comment-891 Dr. Goulu Sat, 17 May 2008 21:09:24 +0000 http://www.joaoferreira.org/2008/01/20/a-square-grid-path-problem/#comment-891 useful for Google Treasure Hunt 2008 at http://treasurehunt.appspot.com/ ... Thanks ! ;-) useful for Google Treasure Hunt 2008 at http://treasurehunt.appspot.com/ … Thanks ! ;-)

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