# Matt Pressland

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bio website people.bath.ac.uk/mdp33 location Bath, United Kingdom age 25 member for 2 years, 10 months seen 17 hours ago profile views 924

Postgraduate student at the University of Bath, UK, studying geometry and representation theory. Currently thinking about cluster algebras and related objects.

# 2,066 Actions

 Sep18 revised Show that all the integer solution of $a^n = b^m$ are given by $a = t^{m/gcd(n,m)}$ , $b = t ^ {n/gcd(n,m)}$ , for some integer $t$. added 5 characters in body; edited title Sep18 reviewed No Action Needed Simpson's Error Bound Estimation Sep18 comment Help with a proof in Hartshorne's book @user42912 One possible point of confusion is that I cheated - $V_Q$ isn't contained in $V_P$ in general, so the right hand side should really have a $|_{V_P\cap V_Q}$ instead of $|_{V_Q}$. Then it's the axiom of presheaves that says restricting twice is the same as restricting all the way to the smallest set in one go. Sep17 reviewed Close Where do I start with these set theory proofs? Sep17 reviewed Close Derivative of an Integral with max in the integrand Sep17 comment Help with a proof in Hartshorne's book @user42912 $\varphi$ is a collection of maps $\varphi(U)\colon\mathscr{F}(U)\to\mathscr{G}(U)$ for each open $U$, but the $(U)$ isn't always written to simplify the notation. All of the sections you consider are defined over open subsets of $U$, so everything makes sense when you replace $\varphi$ by $\varphi(U)$ again. Sep17 comment What is the best response to the reasoning below? I'm not sure that second problem is really a problem - if the reasoning beforehand had been correct, it would follow by specializing to the case $a=1$. However it does (talking to the OP now) suggest that working through the proof with $a=b=1$ might point out where the problem is. (Maybe that was your point?) Sep17 comment Help with a proof in Hartshorne's book @user38268 Ha, that is a fairly extreme level of pedantry! ;-) But it is indeed true that if you want to find the axiom I mean, you probably need to look up presheaves, so edited. Sep17 revised Help with a proof in Hartshorne's book added 3 characters in body Sep17 answered Help with a proof in Hartshorne's book Sep17 reviewed No Action Needed Bounds for expected values. Sep17 comment $f[A\cup{B}]=f[A]\cup{f[B]}$ If you're worried about how $f$ interacts with the set builder notation, you can avoid it completely by proving $f(A\cup B)\subseteq f(A)\cup f(B)$ and $f(A)\cup f(B)\subseteq f(A\cup B)$. But as has already been said, your existing argument is correct. Sep17 answered Explanation on a double summation Sep17 reviewed Reopen What is the correct answer to this answered combinatorics problem? Sep17 reviewed Leave Open Birational and faithfully flat $\implies$ isomorphism Sep17 reviewed Approve Find the tangent to $f(x)$ Sep17 reviewed No Action Needed $b$ uniformly elliptic and bounded $x\mapsto (b(x))^{-1}$ uniformly elliptic and bounded? Sep17 reviewed Close Indexing a vector function, $E(s)=(E_1(s),E_2(s),E_3(s))$, in MATLAB without evaulating the function Sep17 answered Find the tangent to $f(x)$ Sep17 reviewed No Action Needed automorphism of a rooted tree