Quantifier/Examples/Existence of Multiplicative Identity

Example of Use of Quantifiers
Let $x$ and $y$ be in the natural numbers.


 * $\exists x: \forall y: \exists z: \paren {y > z} \implies y = x z$

means:


 * There exists a natural number $x$ such that every natural number $y$ equals the product of $x$ with a natural number $z$.

This is shown to be true by setting $x = 1$.