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Nov
16
comment Eigenvalues, polynomials and minimal polynomials
If $\lambda=0$, $Bv$ could be $0$, in which case your solution your solution to (a) wouldn't work (hence the stated hint). However, note that $det AB = det BA$, so...
Nov
1
comment $A$ is dense in $[0,1]$ and $f(x)=0$ for all $x$ in $A$ then the integral is zero
Are you using Riemann or Lebesgue integrals? The Dirichlet function is not Riemann integrable.
Nov
1
comment How to find a non-Gaussian function f(x) that satisfies the following condition:
Do you mean $\int_0^\infty f(x)^2 dx > 2 (\int_0^\infty f(x)dx)^2$? If so, the problem is much easier, but this function still works.
Oct
21
comment Last 3 digits of $7^{12341}$
Note also that $\varphi(125)=100$, so you really just need $7^{41} (\bmod 125)$.
Sep
8
comment Simple groups in group theory
Simple groups are non-trivial: en.wikipedia.org/wiki/Simple_group
Aug
26
comment What if objective function $Z$ is also in the constraints?
The constraint should instead be $\sum_j y_j = 1$ (there's also a constraint that $y\ge0$). Incidentally, this proves the Minimax Theorem for two-player zero-sum games.
Jun
2
comment If $y=x^{x^{x^{x^{x^{.^{.^{.}}}}}}}$ then how $y=x^y$?
I haven't proven that the tower converges. I proved that $(b_n)$ converges, since the OP asked me to in the comments.
May
31
comment Variant on divergence theorem
@custodia Yes, in particular we can choose $\vec{k}$ to be each of the basis vectors.
May
31
comment Variant on divergence theorem
One way to show the identity is to apply the divergence theorem on $\vec{k}f$, where $\vec{k}$ is a constant vector, and noting that $\nabla\cdot\vec{k}f=\vec{k}\cdot \nabla f$, since $\vec{k}$ is constant.
Oct
16
comment Is it true that $\lvert \sin z \rvert \leq 1$ for all $z\in \mathbb{C}$?
The second equation should read $4i=e^{iz}-e^{-iz}$. The error carries on from there.
Sep
21
comment On the roots of $t^4-6\sqrt3t^3+8t^2+2\sqrt3t-1=0$
Excellent, thanks. For the last sentence, you mean $n=0,1,2,4$.
Mar
30
comment If i randomly select $n+1$ integers smaller that $2n$ , must there include an integer which divisible with one of the others?
I suppose negative integers are not permitted?
Feb
19
comment Conditional probability. What is the meaning of this explanation?
In other words, the solution is $\frac{1}{6}\cdot0.4$.
Feb
12
comment Probability of an event
I suspect what the question really means is that the test returns positive for .95 of the people with diabetes for .02 of the people without.
Feb
9
comment How to find more numbers like this?
If you require cubes, all such numbers are here: oeis.org/A046197.
Feb
9
comment IMO-2012 Problem 6 (Dušan Djukić, Serbia)
See artofproblemsolving.com/Forum/viewtopic.php?p=2737435.
Dec
6
comment Find variance of a normal distribution given 2 probabilites are equal
@Eric May I know which calculator you're using? You just need the function $\Phi(x)$ and the ability to plot a graph. Just plot the graph of $y=2\Phi\left(\frac Ax\right)-\Phi\left(\frac Bx\right)$ and find where it cuts the 'x-axis'. On TI calculators, $\Phi(x)$ is normcdf.
Dec
5
comment Operations for operands with powers of different bases
Not only is $5\neq 2.23^2$, there is also no point in writing it that way. In general, the most reduced form of writing rational numbers is in terms of powers of primes.
Dec
5
comment 6 Women and 5 Men number of positions problem I don't understand
A man cannot start first - there aren't enough men (try it).
Dec
4
comment How to find the solution of a function with 2 variables and find a limit involving $(3^x + 2^x)^{1/x}$
Are you sure you copied the equation of the curve correctly? $x^2+y^2=16(x^2-y^2)$ is just a pair of intersecting lines.