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seen Jul 14 at 4:38

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!
Dec
16
comment Proving that $m^p-m$ is divisible by $p$
A lot of concepts here I'm not familiar with...
Dec
9
comment Limit of $\left(\frac{n^{2}+8n-1}{n^{2}-4n-5}\right)^{n}$, is the following true?
lol yeah... that's right... So I guess it's wrong that $\lim \left(\frac{n^{2}+8n-1}{n^{2}-4n-5}\right)^{n} = (\lim \left(\frac{n^{2}+8n-1}{n^{2}-4n-5}\right))^n$ huh?... Oh after thinking about this for a while (using the answer given after I started typing as well) I think I see why it's wrong. Thanks!
Dec
8
comment Proving that $(1+\frac{x}{n})^n\to e^x$?
hmm that was simple enough. Thank you!
Dec
8
comment Proving that $(1+\frac{x}{n})^n\to e^x$?
Yeah I do. Though I mentioned it, my bad :p
Dec
8
comment Partial limits of sequences
@yoyo for a private case or the general case, how would you prove this is indeed the number of partial limits? (sorry for coming back to such an old question, but I got it as related when about to ask a similar question)
Dec
5
comment $\mathbb{R}\subset\mathbb{F}\subset\mathbb{C}$ implies $\mathbb{F}=\mathbb{R}$ or $\mathbb{F}=\mathbb{C}$?
hmm.. Interesting. But I'm not sure how to conclude $i\in\mathbb{F}$ from that. mind clarifying?
Dec
5
comment $\mathbb{R}\subset\mathbb{F}\subset\mathbb{C}$ implies $\mathbb{F}=\mathbb{R}$ or $\mathbb{F}=\mathbb{C}$?
Oh yeah... You reminded me that we did prove that fields are vector spaces above subfields of themselves. This really does make it a lot simpler. Thank you!
Nov
28
comment $a_{n+1}=\frac{1}{4}+a_n^2$ is converging and have a limit
Thank you! That's a nice trick i didn't know... Too bad classes here doesn't bother to teach you how to solve the exercises you get...
Nov
21
comment Proving $0$ is the limit of $\frac{n}{2^n-1}$ from definition alone
Well, the second way is pretty similar to Pambos's idea, but I really don't feel comfortable with logs. Is it something you expect I'd be introduced to or should I make an effort learn it on my own?
Nov
21
comment Proving a vector space over itself have no subspaces
In the end, after actually understanding how to use the dimensions, I found the other way simpler. But thanks for the help!
Nov
20
comment Proving $0$ is the limit of $\frac{n}{2^n-1}$ from definition alone
Both answers say to use logs, but as of now we never had to use stuff that wasn't thought (or at least shown) in the course apart from basic algebra. Do you think logs enter this definition? Since I most definitly remeber nothing about them from high school...
Nov
19
comment Proving a vector space over itself have no subspaces
Thanks for the edits! English is not my mother language so translating is sometimes difficult for me.
Nov
19
comment Proving a vector space over itself have no subspaces
Ok, that did help me. I now know that if $1_F\in U$ it can't be a vector subspace. But I'm not sure what happens if $1_F\notin U$, since the axioms for vector spaces don't require a vector identity element, right?
Nov
14
comment Proving the sup of $\{\frac{n-m}{n+m}|n,m\in \mathbb{N}, m<n\}$
Though I see how I can use it in this question, appereantly it wasn't necessery. Thanks for this neat idea though, I'm sure it will be useful for me in the future.
Nov
14
comment Proving the sup of $\{\frac{n-m}{n+m}|n,m\in \mathbb{N}, m<n\}$
oh yeah, I see... Damn it's annoying being stuck on a question because you accidently turned a sign around... Thanks!
Nov
7
comment Proving a set of functions from $\mathbb{N}$ to $\{1,0\}$ is countable
actually we didn't talk at all about of $\mathbb{N}^n$ like that. unless I missed a lot more then I can remember