125,926 reputation
1296355
bio website
location Shoulders of Giants
age
visits member for 3 years, 11 months
seen 4 hours ago

The essence of mathematics lies precisely in its freedom. - Georg Cantor

Once you have tasted flight in mathematical skies, you will forever walk the Earth with your eyes turned skyward, for there you have been, and there you will always long to return.


4h
reviewed Leave Open Volume of sphere inside a cylinder
5h
reviewed Leave Open Multiplicative function in Number Theory
6h
comment Let $I$ be an ideal generated by a polynomial in $\mathbb Q[x]$. When is $\mathbb Q[x] / I$ a field?
In a non-field domain, $\,0\,$ is a prime ideal that is not maximal.
8h
reviewed Leave Open sum of two consecutive squares that add up to a square
10h
reviewed Leave Open Category theory as a foundation for mathematics
11h
answered Is it possible to do modulo of a fraction
12h
reviewed Leave Open deriving $y=\sqrt{x+\sqrt{x+\sqrt{x}}\cdots} $
15h
reviewed Leave Open Do Cyclic Polyhedra Maximize Volume?
15h
reviewed Leave Open Localization and direct limit
18h
reviewed Leave Open why the set of ring two-sided ideals coincides with the set of algebraic two-sided ideals in $B(H)$
18h
reviewed Leave Open How large should $a$ be so that $\int_a^{\infty} \frac{dx}{1+x^2} < \frac{1}{1000}$
18h
reviewed Leave Open Frobenius subgroups of Sz(8)
18h
reviewed Leave Open If $\lim\limits_{x \to \infty} f(x) = 1$, can we have function $f(x)$, such that $\int_0^{\infty}f(x)dx$ converges
18h
comment If $a > b$, is $a^2 > b^2$?
@Julian Equivalently it states $\rm\ (a-b)(a+b) \le 0 \iff a+b \le 0\ $ when $\,a>b,\,$ which is true when $\ b < -a < 0\,\ (\iff a+b < 0 < a)$
19h
reviewed Leave Open How to integrate $\int \frac{x^2+\sin x}{2x+\cos x}dx=?$
20h
revised Prove that $\lfloor\lfloor x/2 \rfloor / 2 \rfloor = \lfloor x/4 \rfloor$
added 78 characters in body
20h
revised Is the zero of a field irreducible?
edited body
20h
comment $A+A^2B+B=0$ implies $A^2+I$ invertible?
@aximut Since $\,1\!+\!aa\,$ divides $\,1\!+\!aa\,$ and $\,\color{#c00}a,\,$ it divides $\,1\!+\!aa -\color{#c00}aa,\,$ e.g. see the explicit proof of the special case above.
1d
reviewed Leave Open Extending holomorphic function to neighborhood of square
1d
comment Diophantine equations in $\mathbb{Z}[i]$
@Chris $\ {\rm mod}\ w\!:\,\ \color{#c00}{w\equiv 0}\,\Rightarrow\, \color{#c00}{0\equiv w}\bar w = (5\!+\!2i)(5\!-\!2i) = 29\ \ $