An unfamiliar symbol in the algorithm: what does ∀ mean?

Question

I am reading about an algorithm (this is an A * -based path search algorithm) and it contains a mathematical symbol that I am not familiar with: ∀

Here is the context:

v (s) ≥ g (s) = min _{s'∈pred (s)} (v (s ') + c (s', s)) ∀s ≠ s _{start sub}

Can someone explain the meaning of ∀?

Answer 1

What is the symbol "forall" (for everyone), as shown in the Wikipedia Mathematical Symbol Table or Unicode forall character ( \u2200 , ∀).

Answer 2

The inverted character A is a universal quantifier from predicate logic . (Also see a fuller discussion of first-order predicate calculus .) As others noted, this means that the statements are true "for all cases" of a given variable (here, s). You will soon come across his sibling, the inverse capital E, which is a quantifier of existence, that is, "there is at least one" from a given variable corresponding to the corresponding statement.

If you're interested in logic, you might like the book Logic and Databases: The Roots of Relational Theory from CJ Date. There are several chapters covering these quantifiers and their logical consequences. You do not have to work with databases to benefit from this book cover of logic.

Answer 3

In mathematics, ∀ means FOR ALL.

Unicode character (\ u2200, ∀).

Answer 4

You can read: "For all s such that s is not equal to s [start]"

Answer 5

yes, these are well-known quantifiers used in mathematics. Another example is ∃, which reads as "exists."

http://en.wikipedia.org/wiki/Quantification