Quantifier/Examples/Square of Sum

Example of Use of Universal Quantifier

$\forall x: x \in \R \implies \paren {x + 2}^2 = x^2 + 4 x + 4$

means:

Every real number $x$ satisfies the equation $\paren {x + 2}^2 = x^2 + 4 x + 4$.

Sources

• 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 1$: Some mathematical language: Variables and quantifiers