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Aug
24
comment Proving pointwise convergence to a “Dirichlet-like” function
I am not sure what you mean. Can you elaborate further on your hint? I thought I had answered your questions.
Aug
23
comment Proving pointwise convergence to a “Dirichlet-like” function
Building off of this, would I suppose to the contrary that there is a sufficiently large $N_0$ so that there is an $x \in [0,1]$ for which $f_{N_0}(x) = 0, f(x) = 1$. Taking $n \ge N_0$, I have that for all $\epsilon > 0$, $|f_n(x) - f(x)| \le \epsilon. This can be done as many times as necessary to achieve arbitrary precision. Is this the lines along which you would approach?
Aug
23
comment Proving pointwise convergence to a “Dirichlet-like” function
Do I appeal to the countability of $\Bbb Q$ and show that $|\Bbb Q| = |\Bbb N|$ implies pointwise convergence?
Aug
23
asked Proving pointwise convergence to a “Dirichlet-like” function
Aug
23
accepted Sequence of $C^1[0,1]$ functions $(f_n) \to f$ but $f \notin C^1[0,1]$
Aug
23
comment Sequence of $C^1[0,1]$ functions $(f_n) \to f$ but $f \notin C^1[0,1]$
At least that's what I believe I'm looking for. The "all" would be replaced by "any" if the question was looking for nowhere differentiable right?
Aug
23
comment Sequence of $C^1[0,1]$ functions $(f_n) \to f$ but $f \notin C^1[0,1]$
@Ahriman I'm looking for at least one point.
Aug
23
comment Sequence of $C^1[0,1]$ functions $(f_n) \to f$ but $f \notin C^1[0,1]$
@timur I think that is what I mean by "cusps". For example, $|x|$ has a cusp at $x = 0$.
Aug
23
asked Sequence of $C^1[0,1]$ functions $(f_n) \to f$ but $f \notin C^1[0,1]$
Aug
23
suggested rejected edit on Construct a bijection from $\mathbb{R}$ to $\mathbb{R}\setminus S$, where $S$ is countable
Aug
23
suggested rejected edit on Construct a bijection from $\mathbb{R}$ to $\mathbb{R}\setminus S$, where $S$ is countable
Aug
23
awarded  Excavator
Aug
23
revised Calculate the remainder when there are division
cleaned up substantially
Aug
23
suggested approved edit on Calculate the remainder when there are division
Aug
23
revised Finding $\lim_{x \to \infty} \left[ {x^{x+1} \over (x+1)^x} - { (x-1)^x\over x^{x-1}}\right]$
improved formatting
Aug
23
revised Why do complex functions have a finite radius of convergence?
OCD LaTeXing
Aug
23
suggested approved edit on Why do complex functions have a finite radius of convergence?
Aug
23
suggested approved edit on Finding $\lim_{x \to \infty} \left[ {x^{x+1} \over (x+1)^x} - { (x-1)^x\over x^{x-1}}\right]$
Aug
23
revised Is there a name for $[0,1]$?
OCD LaTeXing
Aug
23
suggested approved edit on Is there a name for $[0,1]$?