Index Page numbers in italics indicate textboxes. A Abelian group, 134, 139­140, 142, 146, 154, 157­158 Addition table, 142­143 Algorithms, division, 16 Alternating sequence, 159 And/or statement, 16­21 Antisymmetric relation, 106 Argument validity, 4­5 Associative operation, 125 Associative property, 121­122, 125­127, 136, 145 D De Morgan's laws, 78, 78, 80, 80, 86 Decreasing function, ix Decreasing sequence, 159, 162 Definition, 2 Diagrams (Venn), 73­74, 76­77, 79 Difference of two sets, 80 Digraph (directed graph), 104­105, 104­105 Direct proof, 9 Divisible, vii Division algorithm, viii Domain of a function, 89, 99, 170 B Bijection (or bijective function), 92­93, 148, 150, 152­154, 179­181 Binary operation, 118­129, 133, 145 Bounded sequence, 160­162 E Elements of a domain, 99 Elements of a set, 71, 82 Equality, 123, 125, 158 Equality of numbers, 66­69 Equality of sets, 72­73 Equivalence class, 109­110, 109, 113­114, 116­117, 142 Equivalence relation, 36, 38, 38­39, 106, 109­111, 114, 116, 142 C Cancellation laws, 138 Cantor's diagonal argument, 186 Cartesian plane, 83