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Math dxe bxc ceiling (the smallest integer greater than or equal to x floor (the largest integer less than or equal to x Boolean Operations ∧ logical AND ∨ logical OR ¬ logical NOT ⊕ logical XOR Set Operations ∅ the empty set ∩ intersection ∪ union A complement of A Ac also the complement of A a∈A a is an element of the set A |A| the size (number of elements) of A A⊆B A is a subset of (possibly equal to) B A(B A is a strict subset (not equal to) B A×B Cartesian product of A and B; consists of {(a, b) : a ∈ A, b ∈ B}. P (S) powerset (set of all subsets) of S 2S also means powerset of S A\B set difference; all the elements of A that are not in B Functions f :A→B ∼ f ◦g and Relations a function f taking as input elements of A and outputting elements of B. a relation function composition: (f ◦ g)(x) = f (g(x)) Strings and Languages ε the zero-length string xn n copies of x x∗ zero or more copies of x x+ one or more copies of x {x, y} x or y xy, x · y x concatenated with y; that is, the string x followed by the string y |x| the length of x Proofs ∀ ∃ for all there exists Additional Resources DeTeXify Draw a symbol and it finds the LaTeX command 1