- published: 23 Jun 2016
- views: 24182
In predicate logic, an existential quantification is the predication of a property or relation to at least one member of the domain. It is denoted by the logical operator symbol ∃ (pronounced "there exists" or "for some"), which is called the existential quantifier. Existential quantification is distinct from universal quantification ("for all"), which asserts that the property or relation holds for any members of the domain.
Symbols are encoded U+2203 ∃ there exists (HTML: ∃
∃
as a mathematical symbol) and U+2204 ∄ there does not exist (HTML: ∄
).
Consider a formula that states that some natural number multiplied by itself is 25.
0·0 = 25, or 1·1 = 25, or 2·2 = 25, or 3·3 = 25, and so on.
This would seem to be a logical disjunction because of the repeated use of "or". However, the "and so on" makes this impossible to integrate and to interpret as a disjunction in formal logic. Instead, the statement could be rephrased more formally as
For some natural number n, n·n = 25.
This is a single statement using existential quantification.
(There is)
(There is)
(There is)
(There is)
(There is the time, there is the place)
(There is the girl, there is the face)
(There is the hand, there is the touch)
(There is the love I need so much)
Oh girl, why won't you let me love you
And let your troubled heart be free
A-take heed a-to all my goodness
Take a hold and follow me now listen, baby
([unintelligible] there is today) yeah, yeah
(I am the road, I am the way) oh...
(I'll fight your fears down through the years) uh-huh!
(Believe me, believe me, baby)
Girl, why won't you let me love you
What does it take to make you see (you got to see, baby)
All the precious time you been a-wastin', baby (you been wastin',
you been wastin')
You coulda been sharing it with me sharing it baby
With every ounce of my love
I have in my command
I'm doing the very best I can
To make you understand whoa, yeah
(There is) you, baby
(There is) and me
(There is) and hope
(There is) and love
(There is) you, you you
(There is) and me
(There is) and hope
(There is)
(This is the time, this is the place) yeah, yeah
(You are the girl, you are the face) all right
(I am the hand, this is my touch) uh-huh!
(There is the love I need so much)
(There is) you...
(There is) and me
(There is) and love