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

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