I am having this set:
$$ X= \mathbb{Q^+} = \{x \in \mathbb{R} \ \ |x \in \mathbb{Q} \ \text{and} \ x>0 \} $$
How can I prove that $\inf X= 0$ and there is no supremum ?
(I think there is no maximum and no minimum in X?)
My attempt: $$ X=]0, \infty[ $$ $$ \implies \inf \ B = 0$$
- For all $ y \in B: y\ge0$
- For all $ x >0 \ \exists y \in \ B:x>y$
My Questions: Is this a correct way to prove the infimum of B? How can I prove that there is no supremum?