Comments for Matt Baker's Math Blog
https://mattbaker.blog
Thoughts on number theory, graphs, dynamical systems, tropical geometry, pedagogy, puzzles, and the p-adicsMon, 17 Apr 2017 18:48:46 +0000hourly1http://wordpress.com/Comment on Real Numbers and Infinite Games, Part II by Matt Baker
https://mattbaker.blog/2014/07/07/real-numbers-and-infinite-games-part-ii/comment-page-1/#comment-1294
Mon, 17 Apr 2017 18:48:46 +0000http://mattbakerblog.wordpress.com/?p=733#comment-1294Thank you, I had left out the word “open”. But in any case the usual formulation of the BCT is just that X itself cannot be meager (if it’s a non-empty complete metric space), so I’ve changed the statement to this.
]]>Comment on Real Numbers and Infinite Games, Part II by Malkym Lesdrae
https://mattbaker.blog/2014/07/07/real-numbers-and-infinite-games-part-ii/comment-page-1/#comment-1292
Sun, 16 Apr 2017 02:12:38 +0000http://mattbakerblog.wordpress.com/?p=733#comment-1292Respectfully, there may be an error in the statement of the Baire Category Theorem. For example, \{0,1,2 \} is a non-empty subset of a complete metric space, but is certainly meager.
]]>Comment on A Celebration of Independence by Matt Baker
https://mattbaker.blog/2015/07/04/a-celebration-of-independence/comment-page-1/#comment-1289
Mon, 10 Apr 2017 13:43:24 +0000http://mattbakerblog.wordpress.com/?p=1120#comment-1289You are correct Tyler, thanks. What I had written is true if one first puts A in a suitable normal form, but that is probably not worth explaining in the post (as it’s not needed), so I’ve simply deleted the incorrect remark.
]]>Comment on A Celebration of Independence by Tyler
https://mattbaker.blog/2015/07/04/a-celebration-of-independence/comment-page-1/#comment-1288
Fri, 07 Apr 2017 17:14:02 +0000http://mattbakerblog.wordpress.com/?p=1120#comment-1288In the discussion of duality, it says: “If $M=M(A)$ is the linear matroid associated to a matrix $A$, then $M^{*}$ is the linear matroid associated to the transpose of $A$.” According to the definition of $M^{\ast}$, both $M$ and $M^{\ast}$ have the same underlying set $E$. On the other hand, in Example 1, linear matroids are defined so that the cardinality of $E$ is the number of columns of $A$. If $A$ is an $m\times n$-matrix, then we should have $\# E=n$, whereas $M(A^{\text{t}})$ should have an underlying set of size $m$. …Maybe I misunderstand.
]]>Comment on Hodge Theory in Combinatorics by Whitney Encounters of the Second Kind | Matt Baker's Math Blog
https://mattbaker.blog/2015/12/14/hodge-theory-in-combinatorics/comment-page-1/#comment-1167
Thu, 05 Jan 2017 16:39:03 +0000http://mattbakerblog.wordpress.com/?p=1227#comment-1167[…] of Adiprasito, Huh, and Katz on the Rota-Welsh conjecture and Hodge theory for matroids. See this previous post for an introduction to their work. My write-up for the Current Events Bulletin is included in […]
]]>Comment on A p-adic proof that pi is transcendental by Số vô tỷ và p-adic – Lý thuyết Hàm Suy Rộng
https://mattbaker.blog/2015/03/20/a-p-adic-proof-that-pi-is-transcendental/comment-page-1/#comment-1138
Mon, 26 Dec 2016 03:21:08 +0000http://mattbakerblog.wordpress.com/?p=371#comment-1138[…] Matt Baker […]
]]>Comment on p-adic Numbers and Dissections of Squares into Triangles by Matt Baker
https://mattbaker.blog/2016/03/24/p-adic-numbers-and-dissections-of-squares-into-triangles/comment-page-1/#comment-932
Wed, 27 Apr 2016 19:16:23 +0000http://mattbakerblog.wordpress.com/?p=1844#comment-932No, unfortunately I don’t know of any other results which can be proved in this way. I don’t actually think of the tropical interpretation as “ad hoc”, but I guess that’s a subjective matter…
]]>Comment on p-adic Numbers and Dissections of Squares into Triangles by Daniele Turchetti
https://mattbaker.blog/2016/03/24/p-adic-numbers-and-dissections-of-squares-into-triangles/comment-page-1/#comment-931
Tue, 26 Apr 2016 18:28:33 +0000http://mattbakerblog.wordpress.com/?p=1844#comment-931This theorem is also one of my favorite applications of p-adic numbers! The tropical interpretation seems a little bit “ad hoc” to me, though: do you know of other results that you can get by coloring planary graphs according to the relative position of the vertices with respect to some tropical curves?
]]>Comment on Probability, Primes, and Pi by Matt Baker
https://mattbaker.blog/2016/03/14/probability-primes-and-pi/comment-page-1/#comment-930
Fri, 15 Apr 2016 20:23:50 +0000http://mattbakerblog.wordpress.com/?p=1620#comment-930That’s a nice argument!
]]>Comment on Probability, Primes, and Pi by Antoine Chambert-Loir
https://mattbaker.blog/2016/03/14/probability-primes-and-pi/comment-page-1/#comment-929
Fri, 15 Apr 2016 19:19:30 +0000http://mattbakerblog.wordpress.com/?p=1620#comment-929There is a nice undergraduate proof of the formula for that runs as follows: for every integer , write , for some polynomial of degree ; its roots are , for , hence , for some constant , hence . Set , one gets . Now let , justifying the limit interchange via, e.g., dominated convergence.
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