I am having trouble understanding how there could be a least upper bound for an open interval. If I have (a,b) and i am looking for the least upper bound X which is the number that is less than or equal to the set of Y such that Y> all the numbers in the interval (a,b) when I think about it I can't understand why it would be b.(adsbygoogle = window.adsbygoogle || []).push({});

If the interval was (1,2) I would first think the lowest upper bound would be just to the left of 2. So 1.9999999 which would be a number with infinite decimals . I don't understand why it would be 2 as my textbooks says.

**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!

# Least upper bound of open interval.

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