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Aug
24
comment Find projection of a point to a ball and box?
For the closed ball, move the coordinates so that the ball is centered at zero. Can you solve it now? It's just polar coordinates... For the box - it is not clear to me what a projection on the box IS. Do you have examples of such a projection?
Aug
23
comment Is $A+nB$ invertible when $A$ is invertible?
A possible direction: For $C_n=A+nB$ to be invertible, you need it's columns to be linearily independent (they need to be a basis for $\mathbb{R}^3$). So, it's basically a problem in proving that you can't have all sets of rows of all $C_n$s all linearily dependent.
Aug
8
comment Area of a Random Polygon
en.wikipedia.org/wiki/Bertrand_paradox_%28probability%29 could help.
Aug
5
comment Range of function $g(x)=\frac{e^{f(x)}-e^{|f(x)|}}{e^{f(x)}+e^{|f(x)|}}$
Try multiplying by the denominator.
Aug
5
revised Why do complex roots come in pairs?
deleted 19 characters in body
Aug
5
answered Why do complex roots come in pairs?
Aug
5
comment Why do complex roots come in pairs?
This also works if you have complex coefficients, you know.
Aug
5
comment Clarification about the concept of number
It was not fringe. It was mainstream (until Aristotelian philosophy took over). Think about the idea of an oath - it is precisely the idea that a lie (wrong signifier) hurts your soul, when uttered in the right circumstances.
Aug
5
comment Clarification about the concept of number
The nice thing about it, is that medieval philosophy (after Plato) assumed that you do put yourself where you sign. And that, if I burn a document with your name on it, I am in fact hurting you. In fact, this view was rather prevalent. Ever heard of voodoo?
Aug
5
answered Clarification about the concept of number
Aug
2
answered What is $0\div0\cdot0$?
Feb
24
answered Topology: Continuous Functions
Feb
23
answered Dirac's delta, infinite series and integral
Feb
23
comment Dirac's delta, infinite series and integral
Tryss, Dirac is a linear integral operator on the space of functions. It is defined as an object which gives you $\int f(x) \delta (x-x_0)dx = f(x_0)$.
Feb
22
comment Dirac's delta, infinite series and integral
Is $p$ a number or a function? If it is a number, then the integral is trivial ($\int \delta(\alpha -i)d\alpha = 1$ iff i is within the integration bounds).
Feb
22
answered How to quickly recognize closed sets and open sets in $\mathbb{R}^2$
Feb
11
answered Verifying that a given set is an ideal
Feb
11
comment Let $a,b$ be positive integers such that $a\mid b^2 , b^2\mid a^3 , a^3\mid b^4 \ldots$ so on , then $a=b$?
So it's really a question of simple arithmetic. If the powers are $x$ and $y$ then what this amounts to is $2ny-y \le 2nx \le 2ny+y$
Feb
11
comment Let $a,b$ be positive integers such that $a\mid b^2 , b^2\mid a^3 , a^3\mid b^4 \ldots$ so on , then $a=b$?
If $a \neq b$ then there can be 2 options - either there is an uncommon prime divisor, or there is only a difference in prime powers. Think about what this means for the powers of prime divisors...
Feb
2
answered Statistics: how to equate two estimators