Reading a book on algorithms. Can someone explain the meaning of the mathematical symbol ∃?
+34
A:
It is called a quantifier. It means "there exists".
When used in an expression such as
∃x s.t. x > 0
It means "There exists a number x such that x is greater than 0."
Its counterpart is ∀, which means "for all". It's used like this:
∀x, x > 0
Which means "For any number x, it is greater than 0."
Welbog
2009-12-23 14:57:21
I thought that was the other way around... Huh. Learn something new every day: http://en.wikipedia.org/wiki/%E2%88%83
Kieveli
2009-12-23 14:58:32
Quantifier. Predicates are something different: http://en.wikipedia.org/wiki/Predicate_(mathematical_logic)
sdcvvc
2009-12-23 14:59:05
@sdcvvc: Righto! Been a few years since my mathematical logic course. :) I've corrected the answer.
Welbog
2009-12-23 15:00:12
This takes me back!
Matt Joslin
2009-12-23 15:01:34
@Kieveli: Backwards "E" for "Exists", upside-down "A" for "All". That should help you, mnemonically.
Randolpho
2009-12-23 15:05:17
Yes and ∀ you can implement complementary to ∃ since ∀x means there is no x not...eg ∀x and ∄x~ are same
LarsOn
2009-12-23 15:10:34
We used a syntax `∀x(x>0)` and `∃x(x > 0)`
Andrew
2009-12-23 15:16:33
@Randolpho Both letters are rotated by 180 degrees, they just happen to have different symmetries.
starblue
2009-12-24 07:55:07
+10
A:
It is the "existential quantifier" as opposed to the upside-down A (∀) which means "universal quantifier." It should be read as "there exists" or "for some". It is a predication that means that some relation or property holds true for at least one object in the domain.
Examples:
An integer n is composite if ∃ integer m such that m > 1 and m < n with n divisible by m.
An integer n is prime if ∀ integer m such that m > 1 and m < n it is true that n is not divisible by m.
A function f is continuous on a metric space (X, d) if ∀x∀ε>0∃δ>0 | ∀y d(x, y) < δ => d(f(x), f(y)) < ε
Jason
2009-12-23 14:59:15
Oh no not the epsilons and deltas! Calculus 1 is flooding back to me now. I have only you to blame, Jason.
Welbog
2009-12-23 15:17:43
Ah, whom am I kidding? I loved Calculus 1. That's why I took Calculus 2 and Calculus 3! Thanks for that trip down memory lane.
Welbog
2009-12-23 15:18:32
Alternating between quantifiers produces formulas which are both hard to understand and hard to handle algorithmically. For example, the definition of continuity has the pattern ∀∃∀ (the ∀x∀y is missing in the example).
starblue
2009-12-24 08:05:37
+2
A:
It is called existential quantifier and being followed by x, it means there exists at least one x
psihodelia
2009-12-23 15:06:30
+1
A:
For future reference, wikipedia has a table of mathematical symbols, with an explanation of the meaning(s) of each one.
Dave Kirby
2009-12-24 14:29:37