Question

Find sup S and inf S, and give reasons for your answers:
S= \[\left\{ x \in \mathbb{Q}:x^4<3 \right\}\]Can I just say here that since Q is not complete, it cannot be bounded, so has no sup or inf?

Answer 1

Or rather there is no rational supremum or infimum of the set, which would be +- (3)^(1/4) in R.

Answer 2

most likely your reasoning is true .. you can't compare complex number with real.
But I'm not sure ..

Answer 3

If we are taking the inf and the sup in \( \mathbb R\) then
inf is \( - \infty \) or it does not exist.
Sup is \( 3^{1/4} \).