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4 out of 5 dentists recommend this WordPress.com siteFri, 05 May 2017 08:48:31 +0000hourly1http://wordpress.com/Comment on Prūfer Group by jheavner724
https://cozilikethinking.wordpress.com/2016/12/30/prufer-group/comment-page-1/#comment-105
Fri, 05 May 2017 08:48:31 +0000http://cozilikethinking.wordpress.com/?p=717#comment-105The Prūfer groups are fun objects. They have lots of cool properties. For instance, they are the only infinite groups whose subgroups are totally ordered by inclusion. They also serve as a nice counterexample to the (false) claim that a group with only finite subgroups must be finite.
]]>Comment on Decisions decisions by ayushkhaitan3437
https://cozilikethinking.wordpress.com/2017/04/26/decisions-decisions/comment-page-1/#comment-104
Fri, 28 Apr 2017 22:21:38 +0000http://cozilikethinking.wordpress.com/2017/04/26/decisions-decisions/#comment-104Peter! So nice to hear from you. We met at the USC Open House, and I had no idea you followed this blog. Good luck at USC!
]]>Comment on Decisions decisions by Peter K
https://cozilikethinking.wordpress.com/2017/04/26/decisions-decisions/comment-page-1/#comment-103
Fri, 28 Apr 2017 21:52:59 +0000http://cozilikethinking.wordpress.com/2017/04/26/decisions-decisions/#comment-103Bummed to hear you won’t be coming to USC!
]]>Comment on Minimal Polynomials of Linear transformations by ayushkhaitan3437
https://cozilikethinking.wordpress.com/2016/10/14/minimal-polynomials-of-linear-transformations/comment-page-1/#comment-88
Fri, 14 Oct 2016 23:29:57 +0000http://cozilikethinking.wordpress.com/?p=612#comment-88Thanks Anurag! I’ve made the required changes
]]>Comment on Minimal Polynomials of Linear transformations by Anurag Bishnoi
https://cozilikethinking.wordpress.com/2016/10/14/minimal-polynomials-of-linear-transformations/comment-page-1/#comment-87
Fri, 14 Oct 2016 12:47:00 +0000http://cozilikethinking.wordpress.com/?p=612#comment-87In the last line of second paragraph, “If the eigenvectors …” you mean eigenvalues and not eigenvectors. There is another typo where you write instead of .
]]>Comment on Projective varieties by Anurag Bishnoi
https://cozilikethinking.wordpress.com/2016/09/30/projective-varieties/comment-page-1/#comment-86
Mon, 03 Oct 2016 12:50:51 +0000http://cozilikethinking.wordpress.com/2016/09/30/projective-varieties/#comment-86It’s not clear to me what you are talking about in the second paragraph. Some explicit examples might help. What exactly do you mean by a polynomial corresponding to a projective variety? If a polynomial f is not homogenous, then how do you make sure implies for all ? In particular, talking about zeros of a non-homogeneous polynomial does not make much sense in projective spaces, unless you talk about the projective closure.
]]>Comment on Slight generalization of the Local Normal Form by Utkarsh Verma
https://cozilikethinking.wordpress.com/2016/07/15/slight-generalization-of-the-local-normal-form/comment-page-1/#comment-81
Sat, 16 Jul 2016 18:04:03 +0000http://cozilikethinking.wordpress.com/?p=550#comment-81Long time.
]]>Comment on Algebraic Geometry 3: Some more definitions by ishanmata
https://cozilikethinking.wordpress.com/2014/12/29/algebraic-geometry-3-some-more-definitions/comment-page-1/#comment-54
Mon, 19 Jan 2015 19:56:17 +0000http://cozilikethinking.wordpress.com/?p=497#comment-54Nice post, Ayush. Just two minor points :
1.) Any functor from an index category has to be faithful. So you may like to replace ‘even if it is neither faithful nor full’ by ‘even if it is not full’ in line 3 para 2.
2.) (para 2 under heading ‘limit’) I think it is better to say ‘an initial object’ rather than ‘the initial object’ to emphasize that a category may have more than one initial object. Of course, any two initial objects have to be isomorphic of course.
]]>Comment on Algebraic Geometry Series 1: An introduction to Category Theory by ayushkhaitan3437
https://cozilikethinking.wordpress.com/2014/12/27/algebraic-geometry-series-1-an-introduction-to-category-theory/comment-page-1/#comment-50
Tue, 06 Jan 2015 02:20:42 +0000http://cozilikethinking.wordpress.com/?p=478#comment-50Ishan after our convesation on facebook, it seems to me that you’re right. I have corrected the error in the main post. Thank you! As always, your comments are invaluable.
]]>Comment on Algebraic Geometry Series 1: An introduction to Category Theory by ishanmata
https://cozilikethinking.wordpress.com/2014/12/27/algebraic-geometry-series-1-an-introduction-to-category-theory/comment-page-1/#comment-48
Mon, 05 Jan 2015 14:07:39 +0000http://cozilikethinking.wordpress.com/?p=478#comment-48Thanks Ayush, but I am not sure I understand this correctly. Below I write some statements according to my understanding, please let me know if I am making some mistake :
1.) Let i : (0,1) \rightarrow (0,2) be the inclusion map. Let F=Hom(-,R) . We get an induced map F(i) : Hom((0,2),R) \rightarrow Hom((0,1),R) . You wish to show that F(i) is not surjective.
2.) The function f:(0,1) \rightarrow R defined by f(x)= \frac{1}{1.5-x} is well defined on this interval and is differentiable (in fact smooth)
3.) f finds a smooth extension g to the interval (0,2). But g can not be given by the same expression on the interval (0,2). g restricts to f on the interval (0,1). Thus (F(i))(g)=f and hence f lies in F(i)(Hom((0,2),R)). Thus this example can not be used to show that the map F(i) is not surjective.
4.) The function h(x)= \frac{1}{1-x} on (0,1) ,on the other hand, does not find a differentiable extension. Thus can not be obtained by restricting a well defined differentiable function on (0,2). This shows that F(i) is not surjective.
Thanks
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