Category:Definitions/Unique Existential Quantifier

This category contains definitions related to Unique Existential Quantifier.
Related results can be found in Category:Unique Existential Quantifier.

The symbol $\exists !$ denotes the existence of a unique object fulfilling a particular condition.

$\exists ! x: \map P x$

means:

There exists exactly one object $x$ such that $\map P x$ holds

or:

There exists one and only one $x$ such that $\map P x$ holds.

This quantifier is called the unique existential quantifier.