Quantifier/Examples/Existence for All of Element Greater Than

Example of Use of Quantifiers

$\forall x: \exists y: x < y$

means:

For every $x$ there exists a $y$ such that $x < y$

or (assuming the domain is that of numbers):

For every number there exists a number greater than it.

Sources

• 1972: Patrick Suppes: Axiomatic Set Theory (2nd ed.) ... (previous) ... (next): $\S 1.2$ Logic and Notation: $(1)$