14,506 reputation
254104
bio website maths.ed.ac.uk/~tl
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visits member for 4 years, 11 months
seen 13 hours ago

Sep
11
reviewed Leave Open Estimates on gamma- functions
Sep
5
comment Is every compact topological ring a profinite ring?
For discussion of this result, see here: golem.ph.utexas.edu/category/2014/08/… . In particular, Todd Trimble gives a very nice, short proof:golem.ph.utexas.edu/category/2014/08/… . I don't know whether it's the same as Ribes and Zalesski's.
Sep
2
awarded  Necromancer
Jul
29
comment Do direct limits (filtered colimits) commute with pullbacks, in C*-algebras?
@ToddTrimble: oh, oops. I didn't think that through. Never mind!
Jul
29
comment Do direct limits (filtered colimits) commute with pullbacks, in C*-algebras?
To find a counterexample, we could start by concentrating on commutative C*-algebras. The full subcategory Comm-C*-Alg of C*-Alg is closed under limits and colimits, so it doesn't matter which category we think of the (co)limits as happening in. Now Comm-C*-Alg is dual to the category CptHff of compact Hausdorff spaces, so to find a counterexample, it's enough to show that inverse lims (cofiltered lims) don't commute with pushouts in CptHff. Taking inverse lims does preserve coproducts and epis in CptHff, so those two simple kinds of pushout won't help us... we need something a bit cleverer.
Jul
28
comment When did coordinate plane “as we know it” come into play?
Imagine if someone nowadays wrote a paper whose title started "An instance of the Excellence of Modern ALGEBRA". You'd immediately dismiss them as a crank. Have we lost something? Or do we just prefer our titles not to sound like Bill and Ted?
Jul
21
revised Is this graph of reciprocal power means always convex?
added 381 characters in body
Jul
21
comment Is this graph of reciprocal power means always convex?
Thanks very much, Dirk and Robert. I agree with Dirk: it's still a puzzle as to why it's so nearly true. E.g. in this particular example, the non-convexity is extremely subtle - I just plotted the graph and couldn't detect it by eye.
Jul
21
accepted Is this graph of reciprocal power means always convex?
Jul
21
revised Is this graph of reciprocal power means always convex?
minor rewording
Jul
21
revised Is this graph of reciprocal power means always convex?
Added detail
Jul
21
revised Is this graph of reciprocal power means always convex?
Corrected math
Jul
21
asked Is this graph of reciprocal power means always convex?
Jul
21
comment Is there a truly general voting impossibility theorem that applies to real elections?
Thanks, Neil, that's really helpful. (And anyone coming late to this thread: please ignore earlier references to specific paragraphs of Neil's answer, which has now been completely rewritten.)
Jul
17
comment Is there a truly general voting impossibility theorem that applies to real elections?
Tim: yes, the empty ballot is certainly included among the "anything" that the voters could do.
Jul
16
awarded  Good Question
Jul
16
comment Is there a truly general voting impossibility theorem that applies to real elections?
@Waldemar: it's true that if you pick a single winner $n$ times, you get a list of $n$ candidates. But it gives $n$ candidates in order, whereas I was asking for an unordered $n$-element set (because that's what's often wanted in practice).
Jul
16
comment Is there a truly general voting impossibility theorem that applies to real elections?
@NeilStrickland: it's not accurate to say that I "want to increase the information content". I'm completely open as to what the voters do inside the booth.
Jul
16
comment Is there a truly general voting impossibility theorem that applies to real elections?
I'm glad to learn the phrase "approval voting"; I'd mentioned marking out of 10 in my question, and this is marking out of 1. But again, this isn't an answer to my question. (I can only apologize that it seems to have been unclear, but I don't see how to make it any clearer.) First, I wasn't looking for any "solution": I was looking for a general impossibility theorem. Second, you're talking about selecting a single winner, and although that's an interesting special case, I was asking about electing a cardinality-$n$ subset of the set of candidates, where perhaps $n > 1$.
Jul
16
awarded  Popular Question