Completeness Axiom, Proving Rationals are not Complete [Real Analysis]

[@user-gn7wb7ht1b]

Shouldn’t x be greater than -(2)^0.5 at 4:57

[@roseline3085]

Good

[@fa6ema989]

I couldn't understand why s cannot the upper bound of S if x^22 ?

[@Juanitoto]

Z⊂R has no supremum