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bio website people.bath.ac.uk/mdp33
location Bath, United Kingdom
age 25
visits member for 2 years, 9 months
seen 11 hours ago

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


Sep
18
comment Property on path-components
@Carpediem Not every subset is a path component, and it wasn't clear they should be subsets of $S$, hence my request for clarification. I'm still a little confused; if you replace "subsets" by "path components of $S$", then there's essentially nothing to prove.
Sep
18
comment Property on path-components
What do you mean by "two points in different subsets"? Which different subsets? Certainly there are points which can be contained in different (even disjoint) subsets of $\mathbb{R}^n$ but are still connected by a path in $S$.
Sep
18
reviewed Approve suggested edit on How do I solve this partial derivative?
Sep
18
reviewed Looks OK Variance of Portfolio Return
Sep
18
reviewed Reviewed Variance of Portfolio Return
Sep
18
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
Sep
18
reviewed No Action Needed Simpson's Error Bound Estimation
Sep
18
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.
Sep
17
reviewed Close Where do I start with these set theory proofs?
Sep
17
reviewed Close Derivative of an Integral with max in the integrand
Sep
17
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.
Sep
17
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?)
Sep
17
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.
Sep
17
revised Help with a proof in Hartshorne's book
added 3 characters in body
Sep
17
answered Help with a proof in Hartshorne's book
Sep
17
reviewed No Action Needed Bounds for expected values.
Sep
17
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.
Sep
17
answered Explanation on a double summation
Sep
17
reviewed Reopen What is the correct answer to this answered combinatorics problem?
Sep
17
reviewed Leave Open Birational and faithfully flat $\implies$ isomorphism