Assuming $s,t,x,z$ are natural numbers, if $s < x$ and $t < z$, then $st < xz$. Prove this.
Do I need induction? Please help.
I am very confused.
Thank you.
2026-03-30 02:11:35.1774836695
Prove if $s<x$ and $t<z$, then $st<xz$.
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This is false; a counterexample would be
$$1 < 2 \;\;\; \text{and} \;\;\; -2 < -1 \;\;\; \text{but} \;\;\; 1(-2) = -2 \not < -2 = 2(-1)$$
In general, though, unless you are limited to have $s,t,x,z \in \mathbb{Z}$, you wouldn't even try to use induction on this. Induction doesn't quite work with real numbers.