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Dec
4
asked Help understanding proof of l'Hospital's rule from Rudin
Dec
2
comment Help understanding Rudin's proof of the chain rule
@Limitless it at least would have been more suggestive
Dec
2
accepted Help understanding Rudin's proof of the chain rule
Dec
2
comment Help understanding Rudin's proof of the chain rule
yeahh I just figured that out immediately after I wrote all this stuff out.
Dec
2
comment Help understanding Rudin's proof of the chain rule
Wow wait I might have figured it out, hah. For fixed t, $\frac{f(t)-f(x)}{t-x}=f'(x)+\text{something}$ where (something) goes to 0 as $x\rightarrow t$. Is that right?
Dec
2
asked Help understanding Rudin's proof of the chain rule
Nov
22
answered Questions with respect to rational functions
Nov
20
comment When $\epsilon$ shrinks, does $\delta$ necessarily? If so, my proof makes sense. If not, can you help me fix it?
Thanks, I got it!
Nov
20
accepted When $\epsilon$ shrinks, does $\delta$ necessarily? If so, my proof makes sense. If not, can you help me fix it?
Nov
20
comment When $\epsilon$ shrinks, does $\delta$ necessarily? If so, my proof makes sense. If not, can you help me fix it?
Sorry, I'm not familiar with the notation $\langle p_n:n\in\Bbb Z^+\rangle$. Is that just some sequence of $p_n$?
Nov
20
asked When $\epsilon$ shrinks, does $\delta$ necessarily? If so, my proof makes sense. If not, can you help me fix it?
Nov
20
revised Validity of my proof for a proposition in Analysis (Tao)
fixed tex formatting
Nov
20
suggested suggested edit on Validity of my proof for a proposition in Analysis (Tao)
Nov
16
accepted Proof that $\lim_{n\rightarrow\infty}\frac{n^\alpha}{(1+p)^n}=0$ from Rudin's Principles of Mathematical Analysis, involving the binomial theorem
Nov
16
comment Proof that $\lim_{n\rightarrow\infty}\frac{n^\alpha}{(1+p)^n}=0$ from Rudin's Principles of Mathematical Analysis, involving the binomial theorem
typo was all mine
Nov
16
revised Proof that $\lim_{n\rightarrow\infty}\frac{n^\alpha}{(1+p)^n}=0$ from Rudin's Principles of Mathematical Analysis, involving the binomial theorem
edited body
Nov
16
asked Proof that $\lim_{n\rightarrow\infty}\frac{n^\alpha}{(1+p)^n}=0$ from Rudin's Principles of Mathematical Analysis, involving the binomial theorem
Nov
16
accepted Help grasping intuitively: if $\{p_n\}$ is a sequence in a compact metric space $X$, then some subsequence of $\{p_n\}$ converges to a point in $X$
Nov
16
comment Help grasping intuitively: if $\{p_n\}$ is a sequence in a compact metric space $X$, then some subsequence of $\{p_n\}$ converges to a point in $X$
Ahh, of course! I forgot exactly what we were trying to prove, hah. This is perfect, thank you so much for your detailed reply. It's funny that there's "not enough room" for a sequence which doesn't converge to a point in $X$ when $X$ is a closed ball, but when you "peel" an infinitely thin layer off of $X$, suddenly there is.
Nov
16
comment Help grasping intuitively: if $\{p_n\}$ is a sequence in a compact metric space $X$, then some subsequence of $\{p_n\}$ converges to a point in $X$
Wow, this really helps! Just one question though—does this depend on the compactness of our disk? What if it was an open disk? Couldn't we make the same argument?