There Exists

A Quantifier. $\exists$ There exists atleast one. It is applied immediately to the free variable after, $\exists x$, rather than for the entire statement similar to how $\neg$ is only for a single term after

Make sure you write a comma, or “such that”, after writing a Mathematical Statement including $\exists$. Example: $\exists x\in R$ such that $x^3<0$. In A31, you will use a comma. In A67, you will use “such that”.

Proof Writing

$\exists x\in D$ such that $D(x)$ Choose x = __ (this could be a variable or concrete value) then prove both $x\in D$ and $P(x)$ is true.

Unique Existence

• Unique Existence