Comments on: Interpolation and the Chinese Remainder Theorem http://www.arsmathematica.net/2007/01/16/interpolation-and-the-chinese-remainder-theorem/ Dedicated to the mathematical arts. Fri, 29 May 2015 09:17:44 +0000 hourly 1 https://wordpress.org/?v=4.1.41 By: Prahlad http://www.arsmathematica.net/2007/01/16/interpolation-and-the-chinese-remainder-theorem/#comment-2092 Mon, 22 Jan 2007 11:55:25 +0000 http://www.arsmathematica.net/archives/2007/01/16/interpolation-and-the-chinese-remainder-theorem/#comment-2092 I have been reading a bit recently about orthogonal functions, and the chinese reminder theorem reminds me a lot of the the theorem of existence of D-sets for linear spaces. In fact the proof and even the solution have a form that is very similar to those I have been reading about.

(see http://books.google.com/books?id=ecS5DKstwREC&dq=fourier+series+and+orthogonal+functions&psp=1)

]]> By: PeterMcB http://www.arsmathematica.net/2007/01/16/interpolation-and-the-chinese-remainder-theorem/#comment-1721 Thu, 18 Jan 2007 00:03:07 +0000 http://www.arsmathematica.net/archives/2007/01/16/interpolation-and-the-chinese-remainder-theorem/#comment-1721 “Mathematics is like drugs, but cheaper.”

Not sure about this — see here.

]]> By: Walt http://www.arsmathematica.net/2007/01/16/interpolation-and-the-chinese-remainder-theorem/#comment-1717 Wed, 17 Jan 2007 22:47:16 +0000 http://www.arsmathematica.net/archives/2007/01/16/interpolation-and-the-chinese-remainder-theorem/#comment-1717 The p-adics can only be reduced mod p^n, not by any other prime. The hypernaturals are close to what I had in mind, but they of course stabilize eventually, just after an infinite number of steps. :-)

]]> By: Wendell http://www.arsmathematica.net/2007/01/16/interpolation-and-the-chinese-remainder-theorem/#comment-1716 Wed, 17 Jan 2007 22:20:33 +0000 http://www.arsmathematica.net/archives/2007/01/16/interpolation-and-the-chinese-remainder-theorem/#comment-1716 Hmmm… Frankly, I don’t think Wendell’s teaching himself very much. But the X-Y reference… that’s, helpful. I can see how that fits. It would also be helpful if Wendell learned some math that deals with sets. (This is a guy who still finds division exciting and mysterious.)

:)

]]> By: a little night musing http://www.arsmathematica.net/2007/01/16/interpolation-and-the-chinese-remainder-theorem/#comment-1714 Wed, 17 Jan 2007 20:45:31 +0000 http://www.arsmathematica.net/archives/2007/01/16/interpolation-and-the-chinese-remainder-theorem/#comment-1714 Yup.

]]> By: Kenny Easwaran http://www.arsmathematica.net/2007/01/16/interpolation-and-the-chinese-remainder-theorem/#comment-1662 Wed, 17 Jan 2007 06:55:59 +0000 http://www.arsmathematica.net/archives/2007/01/16/interpolation-and-the-chinese-remainder-theorem/#comment-1662 Isn’t the fact that the value eventually stabilizes what makes the integer an integer instead of some funny hypernatural, or p-adic thing? And of course, there must be some funny way you can glue these functions together to get a scheme that’s locally a lot like Spec(Z) but got some funny global behavior. At least, that’s what I remember from my first year algebraic geometry class.

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