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 Mar 24 comment Say we have a presentation of a finite group. Does adding additional relations to the presentation always decrease the size of the group? I'll see if I have some time. I don't think you're too far off. The original discussion of completeness is good. Mar 24 comment Say we have a presentation of a finite group. Does adding additional relations to the presentation always decrease the size of the group? happy with your discussion of quotient. What I meant by comparing to linear algebra was why we can reduce the question of "consequence of other relations" to a statement of linearity(because of bases, essentially). Mar 24 comment Say we have a presentation of a finite group. Does adding additional relations to the presentation always decrease the size of the group? This is the "right" answer, but I'd like to see you discuss the quotient. Also, maybe say why this is different than the linear algebra case of "linear dependence". :-) Mar 22 comment 7 Cents and 11 cents Stamps Mathematical Induction Think about the recurrence relation formed by reducing the number by one of the stamp's face value! Mar 3 comment Definition of q-ary lattices Perhaps you could add a definition of q-ary lattice that you're considering? Mar 3 comment Finding an optimal wage Start by observing the equation $9000=600d+200n$. You now have a system of two equations and can maximize $p$. Feb 29 comment Help With a Card Game @pjs36 You're right! the solution is based in projective geometry, the objects are slightly different, but extremely similar to designs. Feb 25 comment Challenging combinatorial problem possibly involving Pigeonhole Principle The question is a bit unclear. First, do you mean the weights can be in the range 1,..,2k? Also, can they repeat? Also, also, does the question want us to use all the weights or some of them? Please try to clean this up. Feb 17 comment Handling data from randomly placed expanding circles @Lovsovs Sorry, I'll be more specific. Edits, coming up. Jul 6 comment An elegant description for graded-module morphisms with non-zero zero component Well, I don't remember. I do remember that I was localizing by these morphisms and that was what I meant by quotienting. Judging by the date, I was probably trying to work out a ncag example. I don't have a clue what it was! Aug 25 comment Why do we use the commutator bracket for Lie algebra's Yes, B R this is also a nice point. Although somehow that seems to depend on some of the other facts. In particular, we define Lie alg reps to be compatible with the structure, which is the Jacobi identity... Nov 25 comment Interesting calculus problems of medium difficulty? @Srivatsan did you consider it for f(x)=x? Jul 23 comment Equalizers in category of sets/graphs — a couple of examples Using latex and a more standard mathematical presentation style. In particular, don't be afraid to write sentences. Jul 20 comment What is the name of the vertical bar in $(x^2+1)\vert_{x = 4}$ or $\left.\left(\frac{x^3}{3}+x+c\right) \right\vert_0^4$? @Zhen Lin, I would say that depends on the usage, I have no spacing issues for using it in set-builder notation or restrictions. Moreover you forgot to mention the \left. However we are deviating quite far from the point of the question. My comment was meant as a joke. Jul 20 comment What is the name of the vertical bar in $(x^2+1)\vert_{x = 4}$ or $\left.\left(\frac{x^3}{3}+x+c\right) \right\vert_0^4$? it's called \mid, at least if you are a TeXnitian. :) Jul 8 comment Direct sum of an algebra and its opposite @Pete L. Clark, yes, this is definitely the thrust of my question, why the heck is it the universal enveloping algebra of anything? Jul 7 comment Direct sum of an algebra and its opposite ok great. Thanks. Jul 7 comment Direct sum of an algebra and its opposite Yes, that is a good point about dimensionality. Can you point me to a statement of this so I can at least remember what I was thinking of? Jul 6 comment How to draw a weight diagram? You have a lot of questions here, and maybe someone will come along and answer them all systematically for your specific example(though you don't tell us what n is), but let me just say this: take a look at chapter 12 of Fulton and Harris, books.google.com/…, I think that reading through this example will make this more clear. Jun 9 comment Mathematical precise definition of a PDE being elliptic, parabolic or hyperbolic @Willie Wong, You're awesome.