⊢QED

Symbols

→

Implication: "if A then B"

∧

Conjunction: "A and B"

∨

Disjunction: "A or B"

¬

Negation: "not A", shorthand for A → ⊥

¬¬A

Double negation: "not not A", which classical logic treats as A

⊥

Bottom: contradiction, the impossible

⊢

Turnstile: "proves" or "yields"

∀

For all: "∀x P(x)" says every x has property P

∃

There exists: "∃x P(x)" says at least one x has property P

=

Equals: two names for the same thing

≠

Not equal: ¬(a = b)

·

Times, for numbers

∈

Is a member of: "x ∈ A" says x is in the set A

⊆

Subset: every member of A is a member of B

∪

Union: in A or in B

∩

Intersection: in A and in B

∣

Divides: "a ∣ b" says b = a · k for some k

≤ <

At most, less than

↔

If and only if: each side implies the other