How to prove such a sequence exists

Let A be a non-empty subset of Y, and let .

If

then there is a sequence of points in A such that converges to x.

Can anyone give me a starting point here? Should I try to prove this by contradiction? I'm just unsure of how to prove a sequence exists...

Re: How to prove such a sequence exists

Quote:

Originally Posted by

**paupsers** Let A be a non-empty subset of Y, and let

.

If

then there is a sequence

of points in A such that

converges to x.

If what sequence would work? (note the terms do not have to be distinct)

If then .

Now you need to explain why that is true.

Re: How to prove such a sequence exists

Thanks... I had actually found a proof that works right after I posted this! I was coming back to say that but you had already commented. :-)