# Lim sup lim inf of rationals in [0,1]

what is the lim sup of the set containing all rationals in the closed interval [0,1] ?
and what is the lim inf?

How do I prove that the value is correct?

## Answers and Replies

LCKurtz
Homework Helper
Gold Member
what is the lim sup of the set containing all rationals in the closed interval [0,1] ?
and what is the lim inf?

How do I prove that the value is correct?
Well, if you think the lim sup might be, for example, 2 [mind you, I'm not saying it is], you would have to show two things:

1. 2 is an upper bound for your set of numbers
2. No number less than 2 is an upper bound for your set of numbers.

In other words, you use the definition. What is your opinion in regard to 2 being the sup? And why? That might get you thinking about what you need to do.

Have you found the limit points of the set of rationals in [0,1]?