B:={ r ∊ Q : r² < 2 } only takes elements from Q. Indeed r² = 1.5 or r²=15/10 are not contained in it. We are viewing B as subset of Q. And looking for a least upper bound in Q (it is the same what we did for the R story but now R is replaced by Q). For B we cannot apply axiom of completeness and (you can prove that) B has no least upper bound in Q