User legionwhale - Mathematics Stack Exchange

21 votes

Can every terminating rational number be approximated with a square root?

answered Sep 18, 2023 at 17:38

7 votes

Does every commutative ring have $2^n$ idempotents?

answered Apr 1, 2023 at 23:36

6 votes

Functional equation $f\left( x^{2}\right) =2f\left( x\right)$and the Cauchy problem $f\left( xy\right) =f\left( x\right) +f\left( y\right)$

answered Sep 15, 2023 at 21:12

4 votes

What if $x$ is in terms of function of $n$, in the expansion of $e^x$?

answered Nov 23, 2022 at 20:07

3 votes

Evaluating $\int_0^{\infty} \frac{\ln (x)}{1-x^n}\text{d}x$

answered Aug 14, 2021 at 20:48

3 votes

Accepted

Proving unique factorization for the set of even numbers

answered Jul 1, 2022 at 18:39

3 votes

Show that $||f_n-f||_p \rightarrow 0$ as $n \rightarrow \infty$

answered Mar 17 at 13:03

2 votes

Is the direct limit of submodules also a submodule?

answered Jul 23, 2023 at 0:28

2 votes

Accepted

Is there anything wrong with this proof that $\lim_{x\to0} \frac{\sin(x)}{x} = 1$?

answered Jul 8, 2022 at 23:48

2 votes

Accepted

Forcing fractional parts to be less than $\varepsilon$ simultaneously

answered Nov 2, 2023 at 2:18

2 votes

Is my proof for $(-(-a)) = a$ correct

answered Nov 28, 2022 at 22:09

2 votes

Accepted

Examples of noncontinuous functions that are continuous intuitively

answered Sep 11, 2023 at 19:06

1 vote

Accepted

If $f: \mathbb{C}\to \mathbb{C}$ is analytic, $f(z) \neq 0$ and $U=\{z \in \mathbb{C} : |f(z)|<1\}$ then the connected components of $U$ are unbounded

answered Jul 24, 2023 at 1:43

1 vote

How can I prove every integer of the form $6^{3k} + 1$ is composite, where k is a positive integer?

answered Feb 23, 2023 at 17:28

1 vote

Can we change the limits for this function?

answered Nov 25, 2023 at 16:45

1 vote

Accepted

Show that a sequence is monotonic.

answered Nov 26, 2022 at 21:53

1 vote

Zeros of an entire function $f(z)$

answered Aug 7, 2022 at 14:29

1 vote

$n$ divides $\sum_{i=1}^ni^k$ for all $k=1,2,...,99$ Prove that $n$ isn't divisible by any number in $\{2,...100\}$

answered Oct 1, 2022 at 12:37

1 vote

Accepted

Let $f$ and $g$ be two positive valued functions defined on $[-1,1]$, such that $f(x)f(-x)=1$, and $g$ is an even function with

answered Apr 3, 2023 at 23:01

1 vote

Accepted

Necessary and sufficient condition for two different metrics $d, d'$ to generate the same topology on $M$

answered Apr 11, 2023 at 2:40

1 vote

An unorthodox way to find cardinalities?

answered Jul 15, 2022 at 2:44

1 vote

What is the proof of this property of integrals involving $e?$

answered Jul 9, 2022 at 0:29

1 vote

Real numbers have at most two decimal expansions

answered Jan 11, 2022 at 22:52

1 vote

Aymptotic formula/closed form for $ \sum_{r=1}^{n} {n \choose r} \frac{f^{(r-1)}(1)}{(r-1)!}$

answered Feb 13, 2022 at 16:24

1 vote

Compactness, open covers and intersection

answered Jun 20, 2022 at 22:44

1 vote

Accepted

Prove that if $f(x)=x^TQx$ is convex then $Q$ is positive semidefinite

answered Oct 16, 2021 at 15:03

1 vote

Prove the inequality $\ln {(1+\frac{1}{x})}> \frac{2}{2x+1}$

answered Jul 28, 2021 at 23:11

1 vote

Accepted

$|p\min(x,q)-y\min(x,w)| \leq x |p-y|?$

answered Mar 17, 2021 at 18:31

1 vote

Changing the interval for alternating series test

answered Mar 17, 2021 at 18:42

1 vote

Some apparently simple algebraic manipulation I just cant figure out ....

answered Mar 18, 2021 at 0:02

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50 Answers

Can every terminating rational number be approximated with a square root?

Does every commutative ring have $2^n$ idempotents?

Functional equation $f\left( x^{2}\right) =2f\left( x\right)$and the Cauchy problem $f\left( xy\right) =f\left( x\right) +f\left( y\right)$

What if $x$ is in terms of function of $n$, in the expansion of $e^x$?

Evaluating $\int_0^{\infty} \frac{\ln (x)}{1-x^n}\text{d}x$

Proving unique factorization for the set of even numbers

Show that $||f_n-f||_p \rightarrow 0$ as $n \rightarrow \infty$

Is the direct limit of submodules also a submodule?

Is there anything wrong with this proof that $\lim_{x\to0} \frac{\sin(x)}{x} = 1$?

Forcing fractional parts to be less than $\varepsilon$ simultaneously

Is my proof for $(-(-a)) = a$ correct

Examples of noncontinuous functions that are continuous intuitively

If $f: \mathbb{C}\to \mathbb{C}$ is analytic, $f(z) \neq 0$ and $U=\{z \in \mathbb{C} : |f(z)|<1\}$ then the connected components of $U$ are unbounded

How can I prove every integer of the form $6^{3k} + 1$ is composite, where k is a positive integer?

Can we change the limits for this function?

Show that a sequence is monotonic.

Zeros of an entire function $f(z)$

$n$ divides $\sum_{i=1}^ni^k$ for all $k=1,2,...,99$ Prove that $n$ isn't divisible by any number in $\{2,...100\}$

Let $f$ and $g$ be two positive valued functions defined on $[-1,1]$, such that $f(x)f(-x)=1$, and $g$ is an even function with

Necessary and sufficient condition for two different metrics $d, d'$ to generate the same topology on $M$

An unorthodox way to find cardinalities?

What is the proof of this property of integrals involving $e?$

Real numbers have at most two decimal expansions

Aymptotic formula/closed form for $ \sum_{r=1}^{n} {n \choose r} \frac{f^{(r-1)}(1)}{(r-1)!}$

Compactness, open covers and intersection

Prove that if $f(x)=x^TQx$ is convex then $Q$ is positive semidefinite

Prove the inequality $\ln {(1+\frac{1}{x})}> \frac{2}{2x+1}$

$|p\min(x,q)-y\min(x,w)| \leq x |p-y|?$

Changing the interval for alternating series test

Some apparently simple algebraic manipulation I just cant figure out ....