Quantifier/Examples/Epsilon-Delta Condition

Example of Use of Quantifiers

$\forall \epsilon: \exists \delta: \forall y: \size {x - y} < \delta \implies \size {\map f x - \map f y} < \epsilon$

means:

For every $\epsilon$ there exists a $\delta$ such that for every $y$:

If $\size {x - y} < \delta$ then $\size {\map f x - \map f y} < \epsilon$.

Sources

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