Symbols:Set Theory/Existential Quantifier

Existential Quantifier

$\exists$

There exists.

$\exists x \in S: \map P x$ means that there exists at least one $x$ in the set $S$ for which the propositional function $\map P x$ is true.

$\exists x: \map P x$ means that there exists at least one $x$ in the universal set for which the propositional function $\map P x$ is true.

The $\LaTeX$ code for \(\exists\) is \exists .

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Appendix: Table $7$: Common signs and symbols: quantifier
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Appendix $14$: Symbols