So if the sequence Rn is the list of all rational numbers in (0,1), how am I to prove that lim inf=0 and lim sup= 1?(adsbygoogle = window.adsbygoogle || []).push({});

I understand that this sequence has sup=1 and inf=0, but since I do not know what the sequence will look like as n approaches infinity, how do I know lim sup=1 and lim inf=1?

For example, if the sequence is non-decreasing, then can I necessarily say that lim inf=0. I know that the inf will be 0, but lim inf cannot be approaching this number since the rational numbers are increasing. Tell me where my thinking is wrong.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Lim inf and lim sup

**Physics Forums | Science Articles, Homework Help, Discussion**