Quantifier/Examples/Epsilon-Delta Condition
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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: $(2)$