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## Existential quantificationIn predicate logic,existential quantification is an attempt to formalize the notion that something (a logical predicate) is true for something, or at least one relevant thing.
The resulting statement is an existentially quantified statement, and we have existentially quantified over the predicate.
In symbolic logic, the existential quantifier (typically "∃") is the symbol used to denote existential quantification.Quantification in general is covered in the article Quantification, while this article discusses existential quantification specifically. ## BasicsThis would seem to be a logical disjunction because of the repeated use of "or". But the "etc" can't be interpreted as a conjunction in formal logic. Instead, rephrase the statement as- For some natural number
*n*,*n*·*n*= 25.
Notice that this statement is really more precise than the original one. It may seem obvious that the phrase "etc" is meant to include all natural numbers, and nothing more, but this wasn't explicitly stated, which is essentially the reason that the phrase couldn't be interpreted formally. In the quantified statement, on the other hand, the natural numbers are mentioned explicitly.
This particular example is true, because 5 is a natural number, and when we put 5 in for
On the other hand, "For some odd number
In symbolic logic, we use the existential quantifier "∃" (an upside-down letter "E" in a sans-serif font) to indicate existential quantification.
Thus if - For some natural number
*n*,*n*·*n*= 25.
Q(n) is the predicate "n is even", then
- For some even number
*n*,*n*·*n*= 25.
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