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bio website mathoverflow.net/users/13832/…
location Chicago, IL
age 20
visits member for 3 years, 6 months
seen May 31 at 6:42

Third year mathematics major at the University of Chicago, currently on leave. My research interest is billiards on polygons. You can contact me about mathematics at acbecker@uchicago.edu. For moderation issues, you will generally get a faster response by raising a flag on this site.


May
5
comment Map preserving intervals but discontinuous
@GillesBonnet What I noticed was that your property is very much like the Intermediate Value Property, and this function is famously discontinuous but satisfies IVP.
May
5
comment Map preserving intervals but discontinuous
This property is stronger than being a closed map however.
May
5
comment Map preserving intervals but discontinuous
@rschwieb It is useful to note that closed intervals are precisely the compact connected subsets of $\mathbb R$.
May
5
answered Map preserving intervals but discontinuous
May
5
revised Integral $\int_0^{\pi/4} \frac{\ln \tan x}{\cos 2x} dx=-\frac{\pi^2}{8}.$
distracting QED removed
May
5
comment $\mathbb{R}$ and $\mathbb{R}\setminus \{0\}$ are not isomorphic as linear orders.
@AsafKaragila Makes sense, I agree.
May
5
revised $\mathbb{R}$ and $\mathbb{R}\setminus \{0\}$ are not isomorphic as linear orders.
edited tags
May
5
comment Is $0.1010010001000010000010000001 \ldots$ transcendental?
IIRC this is a challenge problem in Tools of the Trade by Paul Sally. I remember finding some reference a few years ago (after Sally assigned it to me among a list of problems) to this being open.
May
5
comment Suppose f(x) is an odd function. Prove that g(x) = |f(x)| is an even function.
What is $g(-x)$?
May
5
revised Maximum speed in a circular orbit?
rolled back to a previous revision
May
5
answered Understanding proof that $\pi$ is irrational
May
4
accepted If $K^{\mathrm{Gal}}/F$ is obtained by adjoining $n$th roots, must $K/F$ be as well?
May
4
comment If $K^{\mathrm{Gal}}/F$ is obtained by adjoining $n$th roots, must $K/F$ be as well?
Thanks, I see now that this question is trivial. So the Galois assumption is really quite necessary.
May
4
comment Find $\sup_{f\in F}|f(\frac{1}{2})|$.
Also, I suspect no such $f$ exists; you should instead approximate such a function.
May
4
comment Find $\sup_{f\in F}|f(\frac{1}{2})|$.
Do you mean $f(0)=f(1)=0$, not $f'(0)=f(1)=0$?
May
4
answered Problem understanding the Axiom of Foundation
May
3
comment Is number rational?
@mathh I assumed the OP meant the degree of the extension.
May
3
awarded  Enlightened
May
3
awarded  Nice Answer
May
2
comment Is number rational?
This is quite interesting, and really illustrates how powerful Galois theory is for reasoning about roots of polynomials.