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MathBS's user avatar
MathBS
  • Member for 6 years, 6 months
  • Last seen more than a month ago
4 votes

Prove that $f(x)=\begin{cases}1& \text{if x is rational},\\0 &\text{if x is irrational}\end{cases}$ is discontinuous at every real number.

3 votes

Give an example to illustrate that $\lim_{x\to 0}\ f(x)$ is not always equal to $\lim_{x\to 0}\ f(2x)$

3 votes

Prove that if $\sum{a_n}$ converges absolutely, then $\sum{a_n^2}$ converges absolutely

3 votes

Does ∃ a continuous function $f: [0,1] \to [0, \infty)$ where $\int_0^1 f(x) \; dx = 1$ and $\lim_{n→∞}\int_0^1 f(x)^n \; dx = 0$? (Tifr gs 2022)

2 votes
Accepted

Find the area of ​the figure that is bound by the lines: $y=|x^2-1|$ and $y=3|x|-3$?

1 vote

$G$ a group of odd order. Then $\forall$ $g\in G$ there is $h\in G$ such that $g=h^2$

1 vote

Are there observables $X_1,\ldots,X_m$ and a state $\rho$ in a Hilbert space $H$ of dimension $n$. Prove that rank$(\text{tr}\ \rho X_iX_j))\le n^2$

0 votes
Accepted

Define $g(y)=\int_E f(x+y)\ dx$ where $f:\Bbb{R}^n\to\Bbb{R}$ is Lebesgue integrable on compact sets and $E$ is compact with positive measure.

0 votes

If the set $X$ is linearly independent in and does not span $V=\Bbb{R}^n$ then there is a $v\in V$ s.t. $\{v\}\cup X$ is linearly independent

0 votes

Characteristic function of the Binomial distribution converges to that of the Poisson

0 votes

Testing for Convergence/Divergence using Limit Comparison Test

-1 votes
Accepted

Prove that, the map $x\mapsto=[x]\cos^2{\pi x}$ is discontinuous at every integer points.