Intereting Posts

Bhattacharya Distance (or A Measure of Similarity) — On Matrices with Different Dimensions
Olympiad inequality $\frac{a}{2a + b} + \frac{b}{2b + c} + \frac{c}{2c + a} \leq 1$.
$I\otimes I$ is torsion free for a principal ideal $I$ in domain $R$
Choose 100 numbers from 1~200 (one less than 16) – prove one is divisible by another!
How is it that treating Leibniz notation as a fraction is fundamentally incorrect but at the same time useful?
Sum of odd Bessel Functions
What is the proper way to handle the limit with little-$o$?
Proof/derivation of $\lim\limits_{n\to\infty}{\frac1{2^n}\sum\limits_{k=0}^n\binom{n}{k}\frac{an+bk}{cn+dk}}\stackrel?=\frac{2a+b}{2c+d}$?
How to get solution matrix from REF matrix
Irreducible polynomial over an algebraically closed field
Prob. 9, Sec. 4.3 in Kreyszig's Functional Analysis Book: Proof of the Hahn Banach Theorem without Zorn's Lemma
Intuition – Fundamental Homomorphism Theorem – Fraleigh p. 139, 136
The topology on $X/{\sim}\times X/{\sim}$ is not induced by $\pi\times\pi$.
Integer solutions to $ n^2 + 1 = 2 \times 5^m$
Why is arc length not in the formula for the volume of a solid of revolution?

Consider the two imaginary numbers $i$ and $-i$. Is there any fundamental difference between the two of them? If I take the field $\mathbb{C}$ and apply the map $a + bi \mapsto a – bi$ does the image end up meaningfully different from the field I started with? Or when we write out complex numbers are we arbitrarily choosing which of the non-real solutions to $z^4 = 1$ to call $i$ and which to call $-i$?

- Abelian groups of order n.
- Does there exist any uncountable group , every proper subgroup of which is countable?
- Order of the smallest group containing all groups of order $n$ as subgroups.
- What is the intersection of all Sylow $p$-subgroup's normalizer?
- Order of general linear group of $2 \times 2$ matrices over $\mathbb{Z}_3$
- Prerequisites for studying Homological Algebra
- How is number of conjugacy class related to the order of a group?
- Necessary and Sufficient Condition for a sub-field
- How are lopsided binomials (eg $\binom{n}{n+1})?$ defined?
- Finding a nonempty subset that is not a subgroup

Yes, one of the roots of the polynomial $z^2+1$ is called $i$, the other $-i$; since one is the negative of the other. You can switch the names if you really want to and say that “one root is called $-i$ and the other is called $i$”, but this would not make much difference, right? Traditionally, $i$ is drawn in the upper half-plane and $-i$ in the lower, but this is only a tradition. I am not sure what else would you want to know.

If you have some previous notion of orientation for the plane — some notion of “clockwise” and “counter-clockwise” — then you can specify which solution of $z^2+1=0$ is which. And vice-versa: given a choice of $i$ for $\mathbb C$, you get a corresponding orientation for the plane $\mathbb R^2$ using the usual bijection.

- Proving algebraic sets
- Must an ideal contain the kernel for its image to be an ideal?
- Evaluating a double integral that arises in computing the solid angle subtended by an equilateral triangle
- Explanation of method for showing that $\frac{0}{0}$ is undefined
- Is the curl of every non-conservative vector field nonzero at some point?
- Variance of the sums of all combinations of a set of numbers
- Suppose that $(s_n)$ converges to s. Prove that $(s_n^2)$ converges to $s^2$
- Differential Geometry without General Topology
- Alternative to Axler's “Linear Algebra Done Right”
- Fast $L^{1}$ Convergence implies almost uniform convergence
- Cauchy in measure implies convergent in measure.
- Connecting an almost idempotent complex matrix to a diagonal 1-0 matrix
- Condition on a point on axis of the parabola so that $3$ distinct normals can be drawn from it to the parabola.
- If $G$ is non-nilpotent and $M$ is non-normal subgroup of $G$, then $|G: M|=p^{\alpha}$?
- $n$ choose $k$ where $n$ is less than $k$