Define $s,d,$ to represent supply, demand

Definition of infinite resource:

$$ \forall d, s > d $$

Definition of finite resource:

$$ \exists d, s<d $$

Assuming there is no monopoly, if for some infinite resource, there exists only a finite number of $s$ units in the world, then someone must be able to achieve risk-free arbitrage by producing one additional unit.

This leads to a contradiction $s=s+1$. Therefore, the two assumptions are incompatible.

Q.E.D.