Comments for The Math Less Traveled
http://mathlesstraveled.com
Explorations in mathematical beautyMon, 30 Nov 2015 18:01:30 +0000hourly1http://wordpress.com/Comment on MaBloWriMo 26: Left cosets by MaBloWriMo 29: Equivalence classes are cosets | The Math Less Traveled
http://mathlesstraveled.com/2015/11/27/mablowrimo-26-left-cosets/comment-page-1/#comment-26351
Mon, 30 Nov 2015 18:01:30 +0000http://mathlesstraveled.com/?p=2488#comment-26351[…] will conclude the proof of Lagrange’s Theorem! Recall that we defined subgroups and left cosets, and defined a certain equivalence relation on a group in terms of a subgroup . Today we’re […]
]]>Comment on MaBloWriMo 25: Subgroups by MaBloWriMo 29: Equivalence classes are cosets | The Math Less Traveled
http://mathlesstraveled.com/2015/11/26/mablowrimo-25-subgroups/comment-page-1/#comment-26350
Mon, 30 Nov 2015 18:01:27 +0000http://mathlesstraveled.com/?p=2481#comment-26350[…] will conclude the proof of Lagrange’s Theorem! Recall that we defined subgroups and left cosets, and defined a certain equivalence relation on a group in terms of a subgroup . […]
]]>Comment on MaBloWriMo 28: Equivalence relations are partitions by Brent
http://mathlesstraveled.com/2015/11/29/mablowrimo-28-equivalence-relations-are-partitions/comment-page-1/#comment-26340
Sun, 29 Nov 2015 18:44:31 +0000http://mathlesstraveled.com/?p=2500#comment-26340Good point. Since this is all in the service of proving things specifically about finite groups it doesn’t really matter; partitions with a finite number of parts and equivalence relations on finite sets are indeed in 1-1 correspondence. But you’re right that more generally the definition of a partition should be extended to include the possibility of breaking up infinite sets into infinitely many pieces.
]]>Comment on MaBloWriMo 28: Equivalence relations are partitions by Tom
http://mathlesstraveled.com/2015/11/29/mablowrimo-28-equivalence-relations-are-partitions/comment-page-1/#comment-26339
Sun, 29 Nov 2015 18:35:34 +0000http://mathlesstraveled.com/?p=2500#comment-26339Why the requirement for a partition to be a finite collection of subsets? If you use this restriction then you don’t get a 1-1 correspondence between partitions and equivalence relations like you want.
]]>Comment on MaBloWriMo 24: Bezout’s identity by Brent
http://mathlesstraveled.com/2015/11/25/mablowrimo-24-bezouts-identity/comment-page-1/#comment-26295
Thu, 26 Nov 2015 05:15:00 +0000http://mathlesstraveled.com/?p=2478#comment-26295Yup, good catch, thanks! Fixed now.
]]>Comment on MaBloWriMo 24: Bezout’s identity by Logan
http://mathlesstraveled.com/2015/11/25/mablowrimo-24-bezouts-identity/comment-page-1/#comment-26291
Wed, 25 Nov 2015 23:58:48 +0000http://mathlesstraveled.com/?p=2478#comment-26291When showing that is a common divisor, you state “…that is, evenly divides .” The next sentence states “…shows that evenly divided as well.” Shouldn’t the second be ?
]]>Comment on MaBloWriMo 14: Element orders are no greater than group size by MaBloWriMo 24: Bezout’s identity | The Math Less Traveled
http://mathlesstraveled.com/2015/11/15/mablowrimo-14-element-orders-are-no-greater-than-group-size/comment-page-1/#comment-26283
Wed, 25 Nov 2015 18:51:36 +0000http://mathlesstraveled.com/?p=2430#comment-26283[…] of the month, as suggested by commented janhrcek, we’ll prove the thing I hinted at in an earlier post: namely, that the order of any group element is always a divisor of the order of the group. This is […]
]]>Comment on MaBloWriMo 23: contradiction! by MaBloWriMo 24: Bezout’s identity | The Math Less Traveled
http://mathlesstraveled.com/2015/11/24/mablowrimo-23-contradiction/comment-page-1/#comment-26282
Wed, 25 Nov 2015 18:51:34 +0000http://mathlesstraveled.com/?p=2475#comment-26282[…] the remainder of the month, as suggested by commented janhrcek, we’ll prove the thing I hinted at in an earlier post: namely, that the order of any group […]
]]>Comment on MaBloWriMo 21: the order of omega, part I by MaBloWriMo 24: Bezout’s identity | The Math Less Traveled
http://mathlesstraveled.com/2015/11/22/mablowrimo-21-the-order-of-omega-part-i/comment-page-1/#comment-26281
Wed, 25 Nov 2015 18:51:31 +0000http://mathlesstraveled.com/?p=2463#comment-26281[…] A few days ago we made use of Bézout’s Identity, which states that if and have a greatest common divisor , then there exist integers and such that . For completeness, let’s prove it. […]
]]>Comment on MaBloWriMo 23: contradiction! by Brent
http://mathlesstraveled.com/2015/11/24/mablowrimo-23-contradiction/comment-page-1/#comment-26278
Wed, 25 Nov 2015 14:08:54 +0000http://mathlesstraveled.com/?p=2475#comment-26278Oh, that’s a nice idea!
]]>