Reading a book on algorithms. Can someone explain the meaning of the mathematical symbol ∃?
5 Answers
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."
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
It is called existential quantifier and being followed by x, it means there exists at least one x
For future reference, wikipedia has a table of mathematical symbols, with an explanation of the meaning(s) of each one.
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