Possible Duplicate:
Family of unbounded functions is uncountable.
Definitions:
For functions $f,g:\mathbb{N}\to \mathbb{N}$, we say $f\leq ^{*} g$ if there exist $n\in\mathbb{N}$ such that for $n\leq m$ we have $f(m)\leq g(m)$
Family $F$ of functions from $\mathbb{N}$ to $\mathbb{N}$...
How do I prove that the family of all unbounded functions from $\mathbb{N}$ to $\mathbb{N}$ is uncountable?
One could try to reason by first showing that the set of all functions $\mathbb N\to\mathbb N$ is uncountable, and then removing those that are bounded. This would work if the latter set...
Moreover, the second one has already one delete vote, so we might end with a question closed as a duplicate of a deleted question.
The first question is clearly stated, it explains that it asks about a family of functions which is unbounded w.r.t $\leq^*$.
The second one is rather unclear.
Original version said a family of unbounded functions. But it is very probable that the OP wanted to posted the same question, so Behaviour's edit took it closer to the OP's original intentions.
But still if I read unbounded family, without any further explanation, I would expect unbounded w.r.t. $\le$. (Or I would expect more explanation.)
And the main difference (between the current versions) is that one asks to show that any unbounded family is uncountable and the other one asks to show that the family of all unbounded functions is uncountable.
I don't think Unbounded family of functions from $\mathbb{N}$ to $\mathbb{N}$ should be closed as a duplicate of The family of all unbounded functions on natural numbers is uncountable.
The main difference (between the current versions) is that one asks to show that any unbounded family is uncou...
BTW do you think that in 2015 a new reopen request thread should be open? (And also new tag cleanup thread.)
@IlmariKaronen Difficult to say. I doubt that the reviewer would know. (I am sure that I wouldn't be able to say if someone asked me some detail about some review I did.)
Well, I might report it anyway, if it hasn't been reported already. I'm just wondering if the bug is mostly cosmetic (only affects completed reviews) or actually serious (potentially misleading reviewers).
@MartinSleziak The second question was unclear and had a vote to delete when I found it. My edit aimed at bringing it in line with the accepted answer. I'm not sure what OP's intent really was, but given it's a 2012 question and they did accept Amr's answer, I think it's more important to keep Q&A coherent than to keep guessing at their intentions.
The duplicate link wasn't useful, considering how confused the duplicate target was. Good to see it was unlinked.
