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2d
comment Does Russel's paradox preclude us from using the power set to generate every possible set?
Well as far as I understand, "the set of all things" is not a set, you can't just say "I take everything and call it $A$", and there is actually quite a delicate process describing what is or isn't a set.
2d
comment Fixed point of a differentiable function on a closed interval
@cantorhead, oh well that makes it easy. Thanks!
2d
comment Fixed point of a differentiable function on a closed interval
@GitGud Oh oops, fixed
Apr
14
comment Finding a counter example for $ \left(A+A\right)'\subseteq\left(A'+A\right)\cup\left(A'+A'\right)$
I thought about the idea of searching for a set $A$ with no limit points, such that $A+A$ will have a limit point, but wasn't able to figure one out myself. Even the solution you gave took me quite a while to understand, but I get it now. Thanks!
Apr
3
comment Why can you place in the recursive definition to find the limit?
That makes everything clear. Thank you very much!
Apr
1
comment Finding the limit of $\sqrt[n]{{kn \choose n}}$
Got it! Thanks!
Apr
1
comment Finding the limit of $\sqrt[n]{{kn \choose n}}$
Not quite sure about how you simplified the last step, will try it by hand and come back :P
Apr
1
comment Finding the limit of $\sqrt[n]{{kn \choose n}}$
unfortunately I am unable to follow most of proof 1, and in proof 2 I'm not sure how the lemma gives that $\lim \frac{(kn)!^{1/n}}{(kn)^k} = e^{-k}$, or how you did the algebra...
Mar
23
comment Finding $\sup$ of $\{\sqrt{n} - \lfloor\sqrt{n}\rfloor | n\in\mathbb{N}\}$
hmm I understand that, still not sure how to use it though :P
Mar
23
comment Finding $\sup$ of $\{\sqrt{n} - \lfloor\sqrt{n}\rfloor | n\in\mathbb{N}\}$
Well that's a really nice way of doing it. Didn't think about breaking the number into easier to manage numbers ><
Mar
23
comment Finding $\sup$ of $\{\sqrt{n} - \lfloor\sqrt{n}\rfloor | n\in\mathbb{N}\}$
We haven't actually learned limits yet so I'm not sure how to use this, but it seems to be going to 1? no idea how to prove it though.
Mar
16
comment Proving $2(\sqrt{n} - 1) < \sum\limits_{i=1}^n\frac{1}{\sqrt i}$
Another question, if you don't mind. What was the sign that the original inequality wasn't strong enough for the induction? Is me getting stuck there it or was there something else I need to notice?
Mar
16
comment Proving $2(\sqrt{n} - 1) < \sum\limits_{i=1}^n\frac{1}{\sqrt i}$
hmm, all clear now, though I'm still pretty sure I never would have figured it out myself. Thank you for the help!
Mar
16
comment Proving $2(\sqrt{n} - 1) < \sum\limits_{i=1}^n\frac{1}{\sqrt i}$
Oh yeah I see it, I imagined the reversed order :P. Thank you very much!
Mar
16
comment Proving $2(\sqrt{n} - 1) < \sum\limits_{i=1}^n\frac{1}{\sqrt i}$
I don't understand some of the steps actually, mainly the first (adding the square root of j to the denominator) and the last (going from the sum to n), but it looks pretty neat :)
Mar
16
comment Proving $2(\sqrt{n} - 1) < \sum\limits_{i=1}^n\frac{1}{\sqrt i}$
I'm looking at this and it seems pretty much like what I did, though obviously with \sqrt{n+1} instead of \sqrt{n}, but your induction step gave the elements \sqrt{k+1}-\sqrt{k} in the reverse order compared to mine. Even knowing that I still can't find what I did wrong...
Dec
23
comment limits calculus
This is about the same material where I'm at and I found the following to be a great source, examples are much better and more diversified than those given in class and you can really understand how they got to the solutions. math.ucdavis.edu/~kouba/CalcOneDIRECTORY/preciselimdirectory/…
Dec
23
comment Why does the definition of limits of a function have strict inequality?
Yeah about that part I know, every book and class did even explain it (rather then just giving it as is)
Dec
23
comment Why does the definition of limits of a function have strict inequality?
I actually just commented asking how exactly would you prove it, since I got into a bit of complications of getting rid of the cases of $|x-a|\leq \delta$ and $|f(x)-a|\leq \epsilon$ in the each direction respectively. This clarifies everything nicely.
Dec
23
comment finding a limit of a function by definition
Both solutions really helped me. From what you gave me I was able to realize what my delta needs to be, and the solution below allowed me to understand how I'm supposed to write a proof on these matter. Thank you both!