Least Upper Bound and Supremum

back2square1

Are the least upper bound and supremum of a ordered field same thing? If so, then why do we have two different terms and why do text books do not use them interchangeably. That also means that greatest lower bound and infimum are also the same thing.

oay

Just a couple of expressions to say the same thing.

HallsofIvy

As far as I know "supremum" and "least upper bound" are terms for the same thing. Similarly "infimum" and "greatest lower bound" are terms for the same thing.

Surely you don't think it is unusual to have two different terms for the same thing? And I have never seen a text that did NOT "use them interchangebly" where it used both. Commonly, 'lower level' texts use the English phrase "greatest lower bound" and 'upper level' texts use the latin word "supremum" (which is also commonly used internationally).

back2square1

Thanks you so much. My textbook uses both but they are very specific about where they use which term. And, I'm a beginner in Mathematical Analysis.