Symbols:Set Theory/Universal Quantifier

Universal Quantifier

$\forall$

For all.

$\forall x \in S: \map P x$ means that the propositional function $\map P x$ is true for every $x$ in the set $S$.

$\forall x: \map P x$ means that the propositional function $\map P x$ is true for every $x$ in the universal set.

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

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