The Quantifiers $\forall$ and $\exists$

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Definition (The Quantifiers $\forall$ and $\exists$)

• We'll use $\forall$ as shorthand in place of the phrases "for every," "for all," "for each," or any equivalent expression that suggest for every possible case. We call $\forall$ the universal quantifier.
• We'll use $\exists$ as shorthand in place of the phrases "there exists," "there is at least one," or any equivalent expression that suggest there is at least one possible case. We call $\exists$ the existential quantifier.

These symbols are used often in open discussions, presentations, and informal work. However, when publishing formal papers, it is common practice to avoid using these symbols and instead just write the words.