Analysis Problem: Is x_{0} Element of N Convergent but Natural Number-less?

[math.link]

Let x_{0} element of N. Then there is a sequence (x_{n}) that converges at x_{0} but has no terms that are nutural numbers.

Is that true?

Thank you

 

[Pere Callahan]

Welcome tp PF.

What do you mean by a sequence to converge at some point?

If you ask if a sequence of real numbers all of whose term are not natural numbers can converge to some natural number, the answer is yes. I assume, you prefer trying to prove it yourself to being given a hint right away.

 

[HallsofIvy]

Can you think of a sequence that converges to 0? Does that meet the requirements?