Q.1
Why doesn't the set {x:x2<5} have a supremum in Q ?
Ans:-
Suppose q is a rational number which is an upper bound for your set. Since 5√ is irrational, it must be the case that q>5√ . But then there exists a rational number q′ such that
5√<q′<q
so q couldn't have been a least upper bound.
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