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A Mathematician's Scratchpad

Sunday, February 12, 2006. I seem to be undergoing a bit of a blog diaspora at the moment. The latest instance of this is that, thanks to the generosity of my friends David Jao and Mikael Johansson, A Mathematician's Scratchpad can now be found here. Where I'll be using wordpress 2.0 and - most importantly - LaTeXRender. This way the formulae in my posts can actually be readable. Posted by David R. MacIver at 2:22 AM. Saturday, February 11, 2006. The pressing down lemma. Suppose for every t. Theorem: Giv...

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A Mathematician's Scratchpad | mathsscratchpad.blogspot.com Reviews

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Sunday, February 12, 2006. I seem to be undergoing a bit of a blog diaspora at the moment. The latest instance of this is that, thanks to the generosity of my friends David Jao and Mikael Johansson, A Mathematician's Scratchpad can now be found here. Where I'll be using wordpress 2.0 and - most importantly - LaTeXRender. This way the formulae in my posts can actually be readable. Posted by David R. MacIver at 2:22 AM. Saturday, February 11, 2006. The pressing down lemma. Suppose for every t. Theorem: Giv...

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1 a mathematician's scratchpad

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7 silly proofs 2

8 this satisfies

9 stone duality rocks

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A Mathematician's Scratchpad | mathsscratchpad.blogspot.com Reviews

https://mathsscratchpad.blogspot.com

Sunday, February 12, 2006. I seem to be undergoing a bit of a blog diaspora at the moment. The latest instance of this is that, thanks to the generosity of my friends David Jao and Mikael Johansson, A Mathematician's Scratchpad can now be found here. Where I'll be using wordpress 2.0 and - most importantly - LaTeXRender. This way the formulae in my posts can actually be readable. Posted by David R. MacIver at 2:22 AM. Saturday, February 11, 2006. The pressing down lemma. Suppose for every t. Theorem: Giv...

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mathsscratchpad.blogspot.com

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A Mathematician's Scratchpad: Silly proofs 2

http://mathsscratchpad.blogspot.com/2006/02/silly-proofs-2.html

Sunday, February 05, 2006. I swear this was supposed to be Silly proofs three, but obviously my memories of having done two silly proofs are misleading. This proof isn't actually that silly. It's a proof of the L 2 version of the Fourier inversion theorem. We start by noting the following important result:. Int {-inf} {inf} e {itx} e {-x 2/2} = sqrt{2 pi} e {-t 2/2}. Thus if we let h 0 = e {-x 2}/2 then we have h 0 = h 0 (where denotes the fourier transform). H n' - xh n = -h {n 1}. It will thus suffice ...

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A Mathematician's Scratchpad: October 2005

http://mathsscratchpad.blogspot.com/2005_10_01_archive.html

Wednesday, October 26, 2005. I'm going to stop writing the super-real fields series for now. It's still interesting me, but there are some other subjects which have been bumped up my priorities list recently that I want to learn first. I may well make some posts about them later. Posted by David R. MacIver at 9:44 AM. Saturday, October 08, 2005. Super-real fields 3: Artin-Schreier theory of ordered fields. Also, this approximately completely fails to follow Martin Isaac's Algebra: A Graduate Course.

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A Mathematician's Scratchpad: Super-real fields 3: Artin-Schreier theory of ordered fields

http://mathsscratchpad.blogspot.com/2005/10/super-real-fields-3-artin-schreier.html

Saturday, October 08, 2005. Super-real fields 3: Artin-Schreier theory of ordered fields. I was originally going to use this post to talk about gaps in ordered sets, but I thought I'd detour and talk about Artin-Schreier theory instead. I'm going to need it at some point so I may as well include it now. Also, this approximately completely fails to follow Martin Isaac's Algebra: A Graduate Course. So, which fields have this property? It turns out that the answer is that those elements which are determined...

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A Mathematician's Scratchpad: The pressing down lemma

http://mathsscratchpad.blogspot.com/2006/02/pressing-down-lemma.html

Saturday, February 11, 2006. The pressing down lemma. Let omega 1 be the first uncountable ordinal. A function f : omega 1 - omega 1 is said to be regressive if for every x 0 we have f(x). The pressing down lemma: Every regressive f : omega 1 - omega 1 is constant on some unbounded set. Suppose for every t. We define a sequence x n as follows. Let x 0 = 0. Let x {n 1} = sup { g(t) : t. Now, in particular we have x {n 1} = g(x n). x n. Now, let x = sup x n. We have that f(x). 0 there is some k. The next b...

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A Mathematician's Scratchpad: A Mathematician's Scratchpad

http://mathsscratchpad.blogspot.com/2006/02/mathematicians-scratchpad.html

Sunday, February 12, 2006. I seem to be undergoing a bit of a blog diaspora at the moment. The latest instance of this is that, thanks to the generosity of my friends David Jao and Mikael Johansson, A Mathematician's Scratchpad can now be found here. Where I'll be using wordpress 2.0 and - most importantly - LaTeXRender. This way the formulae in my posts can actually be readable. Posted by David R. MacIver at 2:22 AM. David R. MacIver. London, United Kingdom. View my complete profile. Chains of null sets.

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mathsscratchpad.blogspot.com

A Mathematician's Scratchpad

Sunday, February 12, 2006. I seem to be undergoing a bit of a blog diaspora at the moment. The latest instance of this is that, thanks to the generosity of my friends David Jao and Mikael Johansson, A Mathematician's Scratchpad can now be found here. Where I'll be using wordpress 2.0 and - most importantly - LaTeXRender. This way the formulae in my posts can actually be readable. Posted by David R. MacIver at 2:22 AM. Saturday, February 11, 2006. The pressing down lemma. Suppose for every t. Theorem: Giv...

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