Comments for The Unapologetic Mathematician
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Mathematics for the interested outsiderThu, 14 Jul 2016 15:13:15 +0000hourly1http://wordpress.com/Comment on Properties of Complex Numbers by Peter L. Griffiths
https://unapologetic.wordpress.com/2008/08/08/properties-of-complex-numbers/#comment-30579
Thu, 14 Jul 2016 15:13:15 +0000http://unapologetic.wordpress.com/?p=1082#comment-30579The complex number a+ib has the positive complex ratio a/b, whose arcotangent below 90 degrees can be divided by root n. That is [arcot(a/b)]/n. The cotangent of this result will produce one of the n roots of the complex ratio. This likewise applies to the complex number a-ib and the negative complex ratio -a/b whose negative arcotangent can also be divided by root n. The negative cotangent of this result will produce one of the roots of the negative complex ratio. The circular route of these negative complex ratios is opposite to the route of the positive complex ratios. End.
]]>Comment on Properties of Complex Numbers by Peter L. Griffiths
https://unapologetic.wordpress.com/2008/08/08/properties-of-complex-numbers/#comment-30547
Thu, 07 Jul 2016 16:51:07 +0000http://unapologetic.wordpress.com/?p=1082#comment-30547Further to my comment of 3 August 2013,
[ (1 + 1/r)^n – ( 1 – 1/r)^n]^1/n = 2^1/n [ (*n/1)^1/r + (*n/3)^1/r^3 ….]^1/n.
Let r = 1 so that p = q. This deliberately converts the 3 term assumption into 2 terms.
There can only be equality with 2 terms not the 3 terms assumed in Fermat’s Last Theorem. End
]]>Comment on About this weblog by oldrubbie
https://unapologetic.wordpress.com/about/#comment-30469
Mon, 30 May 2016 22:13:38 +0000#comment-30469I am curious about a blogger who seems to be quite a competent mathematician. He also produces YouTube videos. However, I can find nothing about him. His name appears to be M L Baker and he had spent some time at the Univ of Waterloo. Any clue as to his identity?
]]>Comment on Mac Lane’s Coherence Theorem by RS
https://unapologetic.wordpress.com/2007/06/29/mac-lanes-coherence-theorem/#comment-30457
Thu, 26 May 2016 06:43:31 +0000http://unapologetic.wordpress.com/2007/06/29/mac-lanes-coherence-theorem/#comment-30457I think I’ll try work at it again.Thanks!
]]>Comment on Mac Lane’s Coherence Theorem by RS
https://unapologetic.wordpress.com/2007/06/29/mac-lanes-coherence-theorem/#comment-30456
Thu, 26 May 2016 06:41:28 +0000http://unapologetic.wordpress.com/2007/06/29/mac-lanes-coherence-theorem/#comment-30456Here is my argument: The left quadrilateral gives $\rho_{(A\bigotimes B)\bigotimes1}=\rho_{(A\bigotimes B)}\bigotimes1.$
]]>Comment on Mac Lane’s Coherence Theorem by John Armstrong
https://unapologetic.wordpress.com/2007/06/29/mac-lanes-coherence-theorem/#comment-30449
Wed, 25 May 2016 17:31:28 +0000http://unapologetic.wordpress.com/2007/06/29/mac-lanes-coherence-theorem/#comment-30449If you want to work out a chain of equal morphisms more explicitly, it might help to remember that the associator and the right identor are both natural isomorphisms, so they can be inverted to point the other way.
]]>Comment on Mac Lane’s Coherence Theorem by RS
https://unapologetic.wordpress.com/2007/06/29/mac-lanes-coherence-theorem/#comment-30448
Wed, 25 May 2016 16:58:15 +0000http://unapologetic.wordpress.com/2007/06/29/mac-lanes-coherence-theorem/#comment-30448Yes I know that this is what we are trying to prove, but my question is can you little bit elaborate on it. I was trying to prove it by starting from the lower left corner to the top corner of the triangle and then using in various ways three naturality quadrilaterals. I was unable to use the top triangle identities, and thus couldn’t prove that the central triangle commutes.
]]>Comment on Mac Lane’s Coherence Theorem by John Armstrong
https://unapologetic.wordpress.com/2007/06/29/mac-lanes-coherence-theorem/#comment-30447
Wed, 25 May 2016 14:22:03 +0000http://unapologetic.wordpress.com/2007/06/29/mac-lanes-coherence-theorem/#comment-30447That the triangle near the center commutes is exactly what we’re proving here. The whole outer pentagon commutes, by the pentagon identity, and then we can tile in with various commuting squares and triangles until we get down to the triangle we want to verify.
]]>Comment on Mac Lane’s Coherence Theorem by RS
https://unapologetic.wordpress.com/2007/06/29/mac-lanes-coherence-theorem/#comment-30446
Wed, 25 May 2016 06:43:17 +0000http://unapologetic.wordpress.com/2007/06/29/mac-lanes-coherence-theorem/#comment-30446I can’t see why the triangle near the center commute
]]>Comment on Cotangent Vectors, Differentials, and the Cotangent Bundle by What is a coordinate function $x^i$ of a manifold, given a chart $(U,x)$? - MathHub
https://unapologetic.wordpress.com/2011/04/13/cotangent-vectors-differentials-and-the-cotangent-bundle/#comment-30397
Sun, 08 May 2016 20:12:34 +0000http://unapologetic.wordpress.com/?p=8866#comment-30397[…] I am trying to understand the notes here: https://unapologetic.wordpress.com/2011/04/13/cotangent-vectors-differentials-and-the-cotangent-bundl…. […]
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