What does “$\forall$” mean?

Question

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

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

For all. https://en.wikipedia.org/wiki/Universal_quantification — Michal Adamaszek, Sep 25 '18 at 08:18

score 7 · Accepted Answer · edited Sep 25 '18 at 13:38

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 $0$.

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