How Many Limit Points Does This Function Have?

[Zhang Jiawen]

Let f be a function on [0,major infinity] such that for each point in its graph,(x,y)=(y*y,y).At how many points must each point in f have a limit...?I'm not clear what the question is aiming...

 

[HallsofIvy]

It's a mystery to me! I think "major infinity" must be a translation error but I have no idea what "each point in f has a limit" could mean. In what sense does a point have a limit?

 

[BvU]

Hello Zhang, welcome to PF !

You are not the only one for whom this question is unclear (witness faster typing Ivy's comment!)
My impression is that the problem statement is not quite complete: there remain a lot of questions (some of which may be answered from the context):

Normally functions are a mapping from a domain to an image (or codomain or range).

Your function maps $x \in [0,\infty]$ to what ?
If for each point in its graph x = y^2 that would mean $f: \ x\rightarrow \sqrt x\$ and then the question

At how many points must each point in f have a limit

can easily be answered with "at infinitely many points", but that probably wasn't intended by the exercise writer. He/she may have had in mind one of several possibilities:

1. for all x in the domain $x \in [0,\infty]$
2. idem, except ...
3. still something else

so my return question is: what is discussed in the section/chapter/episode where this exercise is given ?

By the way: I don't believe this "At how many points must each point in f" is literally quoted ...