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9h
comment Another way of doing integration
Arising in your work as an artist? Do tell. And please explain your intuition, since most integrals do not have nice closed form.
9h
comment Can $f''(x)$ exist if $f'(x)$ is undefined?
@copper.hat ... Your answer "No" is for the title, or the question in the body? They have opposite answers.
14h
comment Limit of $\ln(1\cdot\ln(2\cdot\ln(3\cdot\ln(4\cdots))))$
Now looks right.
14h
comment Limit of $\ln(1\cdot\ln(2\cdot\ln(3\cdot\ln(4\cdots))))$
Still wrong. $ 2\cdot\log(x) = \log(x^2)$ where you square all of $x$, not just the first factor.
14h
comment Limit of $\ln(1\cdot\ln(2\cdot\ln(3\cdot\ln(4\cdots))))$
$\ln\ln 2+\ln\ln\ln 3+\ln\ln\ln\ln 4+\dots$ is incorrect
1d
comment Explicit bijection between $\mathbb{R}$ and $\mathcal{P}(\mathbb{N})$
The construction in the proof of Schröder-Bernstein is constructive. So first select two explicit injections and go from there.
1d
comment Show that $\sigma(\mathcal{H})$ is equal to $\mathcal{P}(\mathbb{N})$.
Perhaps you want $\{6\} = A_6 \setminus (\cup_{i=7}^{\infty} A_i)$.
1d
comment Show that $\sigma(\mathcal{H})$ is equal to $\mathcal{P}(\mathbb{N})$.
Next, how about $\{k\}$ for composite $k$?
1d
comment Show that $\sigma(\mathcal{H})$ is equal to $\mathcal{P}(\mathbb{N})$.
Hint: Can you show the singleton $\{47\}$ is in $\sigma(\mathcal H)$?
2d
comment Two disjunct normal subgroups
From what you said, the group $M \times N$ could be much smaller than $G$.
2d
comment Generalization of Liouville's theorem
"Inversion" means: the inverse function, or the reciprocal? It is not postulated that $E_i$ is closed under addition? Well, $E_0$ has exp and log, so addition follows from multiplication. Or, alternatively, multiplication follows from addition, which would be more natural to work with I guess. And reciprocal follows from subtraction.
2d
comment Hard time on understanding real analysis.
Learning mathematics can take a long time. Keep at it. Talk to your instructors. Talk to other mathematics students. Perhaps you will learn to like it. Or perhaps you will find out that you are better suited for opera singing or auto mechanics.
2d
comment Equality in Conditional Jensen's Inequality
The conditions you state for equality in ordinary Jensen are not correct. $\varphi$ need not be linear everywhere, just on the essential range of $X$. That will include the degenerate case.
2d
comment Tweaking the axioms of a Topological Space, what are the consequences?
This definition will work. It defines the collection of closed sets, just as the conventional topology defines the collection of open sets.
2d
comment Tweaking the axioms of a Topological Space, what are the consequences?
User, why don't you try to prove it yourself? Let $\tau$ be a collection of subsets of a set $X$. Then $\tau$ is a topology* if and only if $\{ U : X - U \in \tau\}$ is a topology.
2d
comment Limit of $a_{n+2}=a^2_{n+1}+\frac{1}{6}\cdot a_n+\frac{1}{9}$
Then prove by induction that all terms are $\le 2/3$.
Feb
6
comment Why do we teach Calculus in High School instead of, say, programming?
math.se is not an opinion site. It is not a discussion site. Maybe better try your question at matheducators.stackexchange.com
Feb
5
comment Russell's paradox question
A set cannot belong to itself in ZF set theory. Russel's paradox was a reason for formulating some axioms for set theory, such as the ZF axioms. But Frege's system had no such restriction, which allowed Russel to some up with this paradox. It showed Frege's system of set theory was no good. If $\Omega$ is "the set of all sets" (something Frege's theory allowed) then certainly $\Omega \in \Omega$.
Feb
5
comment Prove that if $f:[a,+\infty [\longrightarrow \mathbb R$ is uniformly continuous, then $\lim_{x\to +\infty }f(x)=+\infty $
Therefore, should be closed as "unclear what you are asking".
Feb
5
comment The closed form of $\int^\infty_{B}e^{-(x+\frac{A}{x})}\,dx$, where $A>0$, $B>0$.
@mk4201 ... Inverse Symbolic Calculator isc.carma.newcastle.edu.au For example: Compute this integral numerically for $B=0$, plug that number into ISC, and get the Bessel answer.