Vhailor
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 Dec 2 awarded Popular Question Oct 12 awarded Enlightened Oct 12 awarded Nice Answer Oct 1 awarded Good Answer Aug 6 awarded Yearling Sep 24 answered Every representation of a finite group is reducible? Sep 24 comment Can a free group over a set be constructed this way (without equivalence classes of words)? In the normal definition of the free group using words, the tedious part is associativity. Using this strategy for the proof, I feel like this complexity is pushed into showing that the "monoid quotient" by (x.i(x)=1) preserves the multiplication in the monoid (so that the quotient is still a monoid). Is there an easy way of proving this? Aug 6 awarded Yearling Nov 16 comment Time in Mathematics Homotopy theory is really all over the place, I probably couldn't give a better reference than Hatcher's Algebraic Topology. For Lie theory, I would suggest John Stillwell's Naive Lie Theory. It only requires linear algebra and calculus and focuses on examples. Aug 6 awarded Yearling Apr 16 comment Nice examples of groups which are not obviously groups The easy way to see that this is a group (and the reason you got downvoted I expect) is that this is easily seen to be a group of matrices because the action of PSL(2,C) matrices on the extended complex plane by möbius transformations is actually just the action of PSL(2,C) on CP^1 by linear transformations, and that is easily seen to be a group if you know the properties of matrix multiplication. Oct 2 accepted $\mu$ on $\mathcal{A}$ is $\sigma$ finite if and only if $\mu$ on $R$ is $\sigma$ finite Sep 29 answered $\mu$ on $\mathcal{A}$ is $\sigma$ finite if and only if $\mu$ on $R$ is $\sigma$ finite Sep 23 comment $\mu$ on $\mathcal{A}$ is $\sigma$ finite if and only if $\mu$ on $R$ is $\sigma$ finite It is a problem in Benedetto and Czaja "Integration and Modern Analysis". I think I found a solution to the problem now, should I post it as an answer here myself? Sep 22 asked $\mu$ on $\mathcal{A}$ is $\sigma$ finite if and only if $\mu$ on $R$ is $\sigma$ finite Aug 6 awarded Yearling Mar 28 answered How can one visualize topological quotients or develop intuition for handling them? Mar 20 comment Applications of the p-adics Measuring the circumference of a circle by knowing its diameter, perhaps? Mar 20 answered Matchings Containing Given Edges Mar 8 comment looking for an imbedding of the Torus in 3-dimensional euclidean space Be careful with this. If you choose the parameters $R=r=1$, then your torus will not have a real hole in the middle (see the "horn torus" picture). Look on the wikipedia page, it says that $R$ is the distance between the center of the "hole" and the center of the "tube" around it, and $r$ is the radius of the tube. If $r \geq R$ then you won't get a real hole, better to choose values like $R=2$ and $r=1$. These radii do not need to be both $1$ since stretching the torus does not change its topology.