"A set X has the least-upper-bound property if and only if every non-empty subset of X has a supremum in X.” from our professor

but going by this definition dosent it necessarily follow that R does not have the least upper bound property?

Moreover, for (0,1) then 1 is the least upper bound which means 0.999999......=1 ?

needlessly ambigious course out of all that ive taken giving truth to what everyone says about anal