find all the subsets of R# which have the property infS=supS

Question

find all the subsets of R# which have the property infS=>supS

anonymous · Answer

Do you have any guesses? What does your intuition suggest?

anonymous · Answer

I mean, by definition we should have that the infS<=supS, so something strange is going on here.

anonymous · Answer

Sorry, I forgot I posted this lol. Yeah I'm confused because I figured that it would be from - infinity to infinity  so how does infs be bigger than sup...

anonymous · Answer

Would it just be none?!

anonymous · Answer

@nerdguy2535

anonymous · Answer

like basically do I just have to prove that there can't be any subsets?

anonymous · Answer

Well, there actually are some subsets where the infS = supS. You just have to be creative.  It lies in the fact that our inequalities aren't strict inequalities. the infS doesn't have to be strictly less than our supS. It could be equal.

anonymous · Answer

Maybe try thinking of mins and maxs to get some intuition going. Are there subsets of N (natural numbers) where the min of the subset equals the max?

anonymous · Answer

(i guess if there is a max)

anonymous · Answer

Like say if the subset was just one point?

anonymous · Answer

That's exactly it :)