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May
17
comment Fermat Last Theorem for non Integer Exponents
You can generalise this to show that the set of real n for which there exist integers $x, y, z$ with $x^n + y^n = z^n$ is dense in $[0,\infty)$.
Nov
17
awarded  Student
Oct
22
comment How does $\sqrt{|e^{-y}\cos x + ie^{-y}\sin x|}= e^{-y}$
As it currently is, the question is wrong, so your answer is at best incomplete. $\sqrt{|e^{-y}\times ...|} = e^{-y/2}$, not $e^{-y}$.
Aug
1
comment Are there any synonyms of “pair of pants” in topology?
I have also heard (and used) trinion, in some conformal field theory papers (we often manipulate Riemann surfaces in 2d CFT).
Aug
1
comment Are non-circular manholes possible?
@J.M. You're right. However, the example of a spiral shows that Hans' question does have answers other than convex constant-diameter domains.
Aug
1
comment Are non-circular manholes possible?
Hans-Peter, a spiral cover to a spiral hole would not pass through I think: doing what J.M. describes would get the spiral stuck after one turn, since the spiral would bang into the ground from below. Actually your way of stating the problem with an infinite plane is a bit odd, since that means that the ground is entirely hollow. A slightly different (but more realistic) situation is if the hole below ground level is $\mathbb{R}^+ \times \text{shape}$ where the shape is part of $\mathbb{R}^2$.
Aug
1
comment Are non-circular manholes possible?
@J.M. I isn't clear: doing it in the naive way would get the cover will stuck when you try to pass the straight part through the hole.
Jul
30
comment Is there a simple explanation why degree 5 polynomials (and up) are unsolvable?
@ErickWong My bad. You are right, let me retract my comment. Perhaps 'if it were possible to "invert" the polynomial $x^5−x$ (i.e. solve $x^5-x=c$ directly like we can $x^5=c$)' would be better?
Jul
29
comment Is there a simple explanation why degree 5 polynomials (and up) are unsolvable?
Can't be $x^5-x$ since that has trivially $0$, $1$, $i$, $-1$ and $-i$ as solutions.
Feb
7
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Feb
7
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