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Doing math.


Feb
24
comment Compactly supported function?
It's from an old article about characterizations of weak convergence for measures.
Feb
24
comment Compactly supported function?
Alright, thanks Harald.
Feb
24
comment Compactly supported function?
Thanks for the counter example. Exactly what I was looking for.
Feb
24
asked Compactly supported function?
Feb
12
comment Monotone nondecreasing homeo => Lipschitz?
Thanks for the counter-example. You posted slightly earlier that Davide, so I'm 'accepting' your answer. Both explain the situation well.
Feb
12
accepted Monotone nondecreasing homeo => Lipschitz?
Feb
12
asked Monotone nondecreasing homeo => Lipschitz?
Feb
8
comment continuous $f:X\rightarrow X'$, $X,X'$ metric spaces properties
What is the definition of acc$(A)$? Also, for b) you can notice that any constant function from $\mathbb{R}$ to $\mathbb{R}$ is a counter-example. Since if $f(x)=c$ for all $x\in \mathbb{R}$, then $f^{-1}\{c\}=\mathbb{R}$ but $\{c\}$ is bounded.
Feb
8
comment Is proving sequential continuity more difficult than proving continuity?
In my experience, showing that a function is NOT continuous can be easier with sequences, here you only need to find one sequence at some discontinuity point. But when showing that a function is continuous, I prefer the $\varepsilon - \delta$ method (or nghoods incase more general setting than metric spaces is considered).
Feb
6
comment $a^m+k=b^n$ Finite or infinite solutions?
Do you mean $a^{m+1}$ or $a^{m}+1$?
Feb
6
comment Why is $\frac{x}{0}$ undefined?
I don't think I quite understand your comment. We know that $0=1-1$ and we only used some basic properties of exponents that are not dependent on the choice of $x$, as long as $x\neq 0$.
Feb
6
revised Why is $\frac{x}{0}$ undefined?
added LaTeX
Feb
6
comment Why is $\frac{x}{0}$ undefined?
$x^{0}=x^{1-1}=\frac{x^{1}}{x^{1}}=\frac{x}{x}=1$ for $x\neq 0$.
Feb
6
suggested approved edit on Why is $\frac{x}{0}$ undefined?
Feb
1
comment Showing that $f$ is continuous
$f$ is in fact uniformly continuous with almost identical proof, or even $N$-Lipschitz by the remark that you made in the beginning.
Jan
31
comment $\mathbb{Q}$ in metric space $(\mathbb{R},d)$ neither open nor closed
@zulon: is $\mathbb{R}\setminus \{0\}$ also a set with empty interioir? I think he meant: $\mathbb{Q}$ and $\mathbb{P}$ both have empty interiors and are complements of each other $\Rightarrow$ both are far from being open and closed.
Jan
30
suggested rejected edit on Union of dense intervals
Jan
30
awarded  Supporter
Jan
30
comment Relationship between x and y
It's not linear, that's for sure, and not logarithm either. What you're looking for could be a very flat exponential function. In fact, there probably exists several different "good" choices and all of them would probably be equally bad in predicting other values. It would require more datapoints to make an accurate predictor.
Jan
30
awarded  Critic