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user432019
  • Member for 6 years, 10 months
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6 votes
3 answers
739 views

How to prove $AB = \{xy \in \mathbb R : x \in A, y \in B\}$ is an open set?

3 votes
1 answer
230 views

Show that if A is a open set or a closed set, then $int(\partial A) = \emptyset$. Also find if the converse is true.

3 votes
1 answer
109 views

Proof verification : $f$ is increasing at $x_0$.

2 votes
1 answer
132 views

Show $\lim_n(x_{n+1} - x_n) = 0$ if $<x_n>$ satisfies $2x_n \le x_{n-1} + x_{n+1}$ for all $n \in \mathbb N$

2 votes
2 answers
118 views

Proof verification : Prove set A is a bounded closed set.

1 vote
1 answer
360 views

Is the set of real numbers between 0 and 1 which only have 1 and 5 in their decimal representation, closed?

1 vote
1 answer
673 views

Proof verification : Closure of the graph of $f(x) = \sin(1/x)$ is not a path connected set.

1 vote
1 answer
68 views

Why $g(a,b) = \|a-b\|$ is continuous?

1 vote
1 answer
103 views

The function that $\lim_{n \to \infty} f(n+x) = 0$, but $\lim_{x \to \infty} f(x) \neq 0$?

1 vote
1 answer
542 views

interior points and limit points of $\{(x,y): x^2+2y^2 < 1\}$

0 votes
1 answer
115 views

Determine the radius of convergence of given power series.

0 votes
1 answer
211 views

Prove $f$ is a continuous function if $e^xf(x)$ and $e^{-f(x)}$ are all monotonic decreasing function

0 votes
0 answers
51 views

Another solution to the problem of finding the interior points and limit points of $A=\{(x,y):x^2+2y^2<1\}$ [duplicate]

0 votes
2 answers
60 views

If $\langle x_n\rangle$ satisfies $\|x_{n+2} - x_{n+1}\| \lt \|x_{n+1} - x_n\|$, can it be a Cauchy sequence?