` 32 D. Mazieres A. GLOSSARYOFNOTATION Notation Name Definition iff Anabbreviation of “if and only if” f ∶ A → B function Function f maps each element of set A to a result in set B. f(x) application Theresult of calculating function f on argument x ā complement Anoverbarconnotes the opposite, i.e., ā is the opposite of a. ⟨a ,…,a ⟩ tuple Astructure (compound value) with field values a ,…,a 1 n 1 n A ∧ B logical and Both A and B are true. A ∨ B logical or At least one, possibly both, of A and B are true. ∃e,C(e) there exists There is at least one value e for which condition C(e) is true. ∀e,C(e) for all C(e) is true of every value e. {a,b,…} set Asetcontaining the listed elements (a,b,…) {e ∣ C(e)} set-builder Thesetofall elements e for which C(e) is true ç emptyset Thesetcontaining no elements ðSð cardinality ThenumberofelementsinsetS e ∈ S element of ElementeisamemberofsetS. A⊆B subset Every memberofsetAisalsoamemberofsetB. A⫋B strict subset A⊆BandA≠B. A 2 powerset Thesetofsets containing every possible combination of members of A, i.e., 2A = {B ∣ B ⊆ A} A∪B union Thesetcontaining all elements that are members of A or members of B, i.e., A ∪ B = {e ∣ e ∈ A ∨ e ∈ B} A∩B intersection Thesetcontaining all elements that are members of both A and B, i.e., A∩B={e∣e∈A ∧ e∈B} A⧵B set difference Thesetcontaining every element of A that is not a member of B, i.e., A⧵B={e∣e∈A ∧ e∉B} ̸ not Negates a symbol’s meaning. E.g., e ∉ A means e ∈ A is false, while ∄e,C(e) means no e exists such that C(e) is true.