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Nov
25
asked Proving that if $a_n\in\mathbb{Z}$ for all $n$ then it's limit is also in $\mathbb{Z}$?
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
accepted Proving $0$ is the limit of $\frac{n}{2^n-1}$ from definition alone
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
21
accepted Proving a vector space over itself have no subspaces
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
20
asked Proving $0$ is the limit of $\frac{n}{2^n-1}$ from definition alone
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
19
asked Proving a vector space over itself have no subspaces
Nov
14
accepted Proving the sup of $\{\frac{n-m}{n+m}|n,m\in \mathbb{N}, m<n\}$
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
14
asked Proving the sup of $\{\frac{n-m}{n+m}|n,m\in \mathbb{N}, m<n\}$
Nov
12
awarded  Commentator
Nov
7
accepted Proving a set of functions from $\mathbb{N}$ to $\{1,0\}$ is countable
Nov
7
revised Proving a set of functions from $\mathbb{N}$ to $\{1,0\}$ is countable
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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.