I hope you are doing well!
I am doing a proof in elementary Real Analysis and wanted to explain my thought thus far:
Proof: By contradiction, suppose not. Then $\forall p \in \mathbb{N}$, we have $s \geq p$ or $p \leq t$.
I tried to go through the first case ($s \leq p$), but am having trouble at arriving to a contradiction. I believe I have to use the Archimedean Property of Real Numbers somehow. Could anyone please let me know if I am on the right track? If I am completely off, would someone please explain, in a basic way, how you would go about this proof?
Thank you and cheers!