Matthew Pressland
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 Oct 24 comment Group objects in category of $\mathcal{Set}$ are groups - How to prove it? As pointed out in the answer, the points of a set $G$ can be naturally identified with the maps $X\to G$ where $X$ is any one-point set. Oct 24 comment Group objects in category of $\mathcal{Set}$ are groups - How to prove it? Here "defines a group" means that the set $G(Z)$ is a group under the binary operation $g\times g'=\mu\circ(g,g')$. (The notation is a bit confusing here; the first $(g,g')$ is a pair of morphisms that you're multiplying to define the group structure on $G(Z)$, whereas the $(g,g')$ in $\mu\circ(g,g')$ is the pair considered as a single map $Z\to G\times G$, by $z\mapsto(g(z),g'(z))$). Oct 24 revised Quick question: Chern classes of Sym, Wedge, Hom, and Tensor added 33 characters in body Oct 24 comment For which $x$ is $e^x$ rational? Transcendental? @pbs Thanks, that's clearer. Oct 24 comment For which $x$ is $e^x$ rational? Transcendental? All transcendental numbers are irrational, so I'm not sure what the role of the "or" is here. Did you mean to ask if $e^x$ is transcendental whenever $x\ne\log{a}$ for some $a\in\mathbb{Q}$? Oct 24 comment Finding the co-ordinate vector You seem to have swapped the roles of $x_1,x_2,x_3,x_4$ and $d,c,b,a$ from the question, which is maybe a little confusing! Oct 24 comment Finding the co-ordinate vector I think you might have a typo (or a confusion) in the last line as well - the solution is finding $x_1,x_2,x_3,x_4$, not $a,b,c,d$, which are arbitrary real numbers. Oct 24 answered Finding the co-ordinate vector Oct 24 comment Finding the co-ordinate vector I don't think you meant for $v$ to be what you wrote - perhaps $v=a+bt+ct^2+dt^3$? Oct 24 revised Finding the co-ordinate vector deleted 18 characters in body Oct 24 revised How to Prove that these Spaces are not Homotopically Equivalent added 37 characters in body Oct 24 comment Show that $G$ is $2$-connected but not necessarily Hamiltonian Yes - this is fine! A graph is $n$-connected if you can delete any \$k