[b]A-1/[/b] A sequence of real functions $f_n \in C^2(\mathbb R)$ with $\exists h \in C(\mathbb R), \forall n\in \mathbb N, f_n '' \leq h$, and the sequence simply converge to $g$.
Is-it true that $g$ is continuous ?
[b]A-2/[/b] A sequence of real functions $f_n \in C^1(\mathbb R)$ with $\exists h \in C(\mathbb R), \forall n\in \mathbb N, f_n ' \leq h$, and the sequence simply converge to $g$.
Is-it true that $g$ is continuous in $\mathbb{R}-A$ with $\text{card}(A) \leq \text{card}(\mathbb N)$ ?
Is-it true that $g$ is continuous ?
[b]A-2/[/b] A sequence of real functions $f_n \in C^1(\mathbb R)$ with $\exists h \in C(\mathbb R), \forall n\in \mathbb N, f_n ' \leq h$, and the sequence simply converge to $g$.
Is-it true that $g$ is continuous in $\mathbb{R}-A$ with $\text{card}(A) \leq \text{card}(\mathbb N)$ ?
When I first read Set Theory by Jech, I came under the impression that the Universe of Sets, $V$ was a fixed, well defined object like $\pi$ or the Klein four group. However as I have read on, I am beginning to have my doubts. We define
$V_{0}:=\emptyset$ .
${\displaystyle V_{\beta +1}:={\mathc...
Reason for asking this question.
Prof. D. C. McCarty recently gave an interesting
interview (published in January 2015, and easily
found on a large video hosting site), entitled
What are the limits of mathematical explanation?
I think this is the best interview with a
philosopher that I h...
