Existential quantification

An Existential quantification of a property over a set is true, if the property is true for at least one element of the set. An existential quantification is usually written with ∃.

Examples: For the set N of natural numbers, ∃x:x²=25 is true, since there is a natural number (namely 5) that can be filled in for x such that x²=25. Likewise, ∃x:x²>25 is also true, since there is a natural number (in fact a whole lot of them, for which the square is greater than 25. On the other hand, ∃x:x²=2 is false (for the natural numbers), since there is no number that can be filled in for x to make the equation true.