3,615 reputation
318
bio website maths.ox.ac.uk/contact/…
location Oxford, United Kingdom
age 24
visits member for 2 years, 8 months
seen Sep 26 at 20:25

My hobbies include doing research mathematics, doing elementary mathematics, writing things in latex, cooking, correcting grammar, and being skeptical. Fortunately there is a stackexchange website for each of these compulsions.


1d
awarded  Explainer
Jul
29
comment When is there a ring structure on an abelian group $(A,+)$?
Here is an argument for $\mathbb{R}/\mathbb{Z}$: If $(\mathbb{R}/\mathbb{Z},*)$ were a ring with unit $u$ then since $\mathbb{R}/\mathbb{Z}$ is divisible there would exist an element $v$ such that $2v=u$, but then $1/2 = u*(1/2) = 2v*(1/2) = v*1 = 0$, a contradiction.
Jul
2
awarded  Curious
Jul
1
awarded  Autobiographer
Jun
14
answered Does the shift operator on $\ell^2(\mathbb{Z})$ have a logarithm?
Apr
25
comment Algebra over a Field
@ArpitaKorwar The comment meant "let $\mathbb{A}$ be any algebra over $F$ with multiplication defined by $xy=0$ for all $x$ and $y$".
Mar
24
comment Proof of $\lim_{n \to \infty} {a_n}^{1/n} = \lim_{n \to \infty}(a_{n+1}/a_n)$
@WimC Thanks. I corrected it now: I meant take any $\alpha>1$.
Mar
24
revised Proof of $\lim_{n \to \infty} {a_n}^{1/n} = \lim_{n \to \infty}(a_{n+1}/a_n)$
edited body
Mar
24
answered Proof of $\lim_{n \to \infty} {a_n}^{1/n} = \lim_{n \to \infty}(a_{n+1}/a_n)$
Mar
3
comment Question over regular induction: Let $P(n)$ be the statement that $n$-cent postage can be formed using just 4-cent and 7-cent stamps
Prove strong induction using regular induction and then use strong induction.
Feb
7
revised Convergence of the sequence $\frac{1}{n\sin(n)}$
added 869 characters in body
Feb
7
comment Convergence of the sequence $\frac{1}{n\sin(n)}$
The statement about random $x$ was only intended to inform any conjecture about $\pi$, which often behaves as though it were random.
Feb
6
comment Convergence of the sequence $\frac{1}{n\sin(n)}$
It seems likely that the upper limit is infinite (even if the irrationality measure of $\pi$ is $2$, which it probably is). One can show that if $x$ is random then the upper limit of $1/|n\sin(x\pi n)|$ is almost surely infinity.
Feb
6
answered Convergence of the sequence $\frac{1}{n\sin(n)}$
Jan
27
awarded  Yearling
Jan
7
reviewed Approve suggested edit on What is a supremum?
Jan
6
reviewed Approve suggested edit on If the leading coefficient of a polynomial is $x^{3}$, does it mean that the graph would always intersect the $x$ axis at $3$ points?
Dec
6
revised Lower central series of a free group
edited body
Dec
1
comment Defintion of $\ell^\infty$
See en.wikipedia.org/wiki/Sequence_space.
Nov
6
comment Taylor's theorem: $f'' + f = 0, f(0) = f'(0) = 0$.
As far as doing it without Taylor's theorem, multiply by $f'$ and integrate, getting $f^2 + f'^2 = \text{const}$. The initial condition implies that the constant is $0$. But since squares are nonnegative, we must have $f\equiv 0$.