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Thomas Oléron Evans
2.7K posts
Thomas Oléron Evans
@Mathistopheles
Maths. Puzzles. Lecturer at @CASAUCL. I've also written a book w/ @Fryrsquared on the merry Maths of Christmas! https://t.co/A3Y2uf96yi
London Beigetreten Ekim 2011
649 Folgt919 Follower
@MattBecker82 Well done. I did prove that these were the only solutions, but I had to prove for a>c>1, a>1 c<-1, c<a<-1 separately, all for |b|>1, having already considered all cases with |a|, |b|, |c| <2. Might post if I get the time, but this margin and all that.
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@Mathistopheles I think that may be all the cases. I’m looking at ruling out solutions where a,b,c>1.
Any solution must have (b^a)/(ln a) = (b^c)/(ln c).
One approach may be to consider the function f(x)=(b^x)/(ln x) and show it is monotonic for x>=2.
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There are three families of solutions. One very easy to find, one fairly easy, and one a bit more tricky.
(And then there's the rigmarole of proving that there are no others, which was less straightforward than I'd anticipated...)
#puzzle #puzzles #maths #math
Thomas Oléron Evans@Mathistopheles
MATHS PUZZLE: Find all integer solutions of: a^(b^c) = c^(b^a) Some clarifications in the following tweet. #maths #math #puzzles
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PS. I should have said "greatest" rather than "largest". Basically, always return the positive real root when there is also a negative real root.
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If there are no solutions, why? If there are finitely many solutions, can you list them? If there are infinitely many solutions, can you describe them all?
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@MattSingh_ You should hear their Eurovision commentary...
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Bloody hell, the French swimming commentators make the Dutch F1 commentators sound impartial
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@Jay42_SD @keiranpedley Yes, my understanding is that polls were particularly accurate overall in both 2018 & 2022: fivethirtyeight.com/features/2022-… This poses a question of whether there is some specific issue of polling when Trump is a candidate, and whether pollsters might (over?)correct for that in 2024.
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@Mathistopheles @keiranpedley Well during the 2022 midterms state pollsters overstated republicans quite often.
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I really wish I could express how meaningless some of these ‘leads’ are. What you’ve got here is 4 tossups and Arizona and Harris can win without Arizona.
Upshot: tune out until post Dem convention. When Harris is actually the nominee and has a running mate.
Emerson College Polling@EmersonPolling
SWING STATE POLLS with @thehill Harris v. Trump Arizona: Trump 49%, Harris 44% Georgia: Trump 48%, Harris 46% Michigan: Trump 46%, Harris 45% Pennsylvania: Trump 48%, Harris 46% Wisconsin: Trump 47%, Harris 47% emersoncollegepolling.com/july-2024-swin…
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@keiranpedley Do we have any idea how aggressive pollsters are being on trying to correct for underestimates of Trump's vote in 2016 and 2020? Fingers crossed for a Labour 2015 to 2017 type polling effect...
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Ps. those that follow US will also know state polling in some of these states has been ropey at best in recent elections. So that’s in Trumps favour in theory but not all polling misses are in the same direction.
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A plot of Labour & Conservative polling errors in all final GB general election voting intention polls, 1945-2024. 2024 polls in red. Data from PollBase (@markpack). #GE24 #politics #stats
Steve Akehurst@SteveAkehurst
Definitely agree with @Dannythefink that GE24 polling miss should be taken more seriously. But in fairness to pollsters: - Several averages had Lab at 37-38%, wide on their lead by ~6% not 10. Bad not catastrophic. - They did pick up late dip in Lab’s vote; it was ignored
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