Quantified Statements

missed intro because of bad internet

• For all/every/each $x \in S, P(x)$ is written $\forall x \in S, P(x)$
  • universal quantifier
• There exists/is/for some/at least one/ $x \in S$ such that $P(x)$
  • $\exists x \in S, P(x)$
  • existential quantifier

$$~[\exists x \in \mathbb{R}: x^2=3] \iff \forall x \in \mathbb{R}: x^2 \neq 3$$