What does “$\forall$” mean?

Question

I am studying cryptography and in the first lesson I saw "$\forall$" element in the following formula:

$\forall x\neq x_0:P(X) = 0$

• What does $\forall$ mean?

Answer 1

It's one of the two "quantifiers" used in math and is read as "for all". Even the latex symbol for it, $\forall$, is obtained by writing $\forall$.

The other quantifier, $\exists$ ($\exists$), is read as "there exists".

The statement $$\forall x\neq x_0:P(x)=0$$ can be translated into English as:

For all $x$ which are not equal to $x_0$, the expression $P(x)$ is equal to $0$.

Further reading