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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
Nov
7
comment Proving a set of functions from $\mathbb{N}$ to $\{1,0\}$ is countable
I tried looking at the private case of $|f^{-1}(\{1\})|=1$, But I'm not exactly sure how to write it. I understand that exists a function $g$ that maps every $n\in\mathbb{N}$ to the function for which $f(n)=1$, but how do I write it formally?
Nov
6
comment Proving a set of functions from $\mathbb{N}$ to $\{1,0\}$ is countable
Yep, these are the functions I try to prove there are countably infinite number of.
Nov
4
comment proving a simple function is bijective
If you'll look at the edit you'll see that's exactly where I was when asking in the first place. Well, it's my fault for trying to post questions while on a bus. I got my answer I think , ty...
Nov
4
comment proving a simple function is bijective
how do I explain this function is infact bijective?
Nov
3
comment Using the AM-GM inequality on 2 elements to deduce it's true for 4?
Got it, thanks...
Nov
2
comment In field ($F, +, \cdot$) , how can I prove $x^2 =1\implies x=1,-1$
still feeling stupid... Thanks for the quick response both of you.
Nov
2
comment In field ($F, +, \cdot$) , how can I prove $x^2 =1\implies x=1,-1$
wow, that was so simple I feel stupid now... Thanks