Bridge to Abstract Mathematics: Mathematical Proof and Structures
Index A complement, 100,175,214,219 Abelian group, 75,99 Absolute maximum and minimum, 157 Absolute value in an ordered field, 3 ...
384 INDEX Associative property (continued) of multiplication, 15, 295, 338 of subtraction (invalidity of), 154 of symmetric diff ...
INDEX 385 of composition (invalidity of), 261 of conjunction, 68 of disjunction, 68 of intersection, 32,40, 123 of multiplicatio ...
386 INDEX Decreasing collection of sets, 125, 290 Dedekind, Richard, 330 Dedekind cuts, 329 Definitionfs), 1 15 inductive, 333, ...
INDEX 387 Equivalence class, 228, 238, 240 representative of, 228, 344 Equivalence classes of Cauchy sequences, 356 product of, ...
388 INDEX Greatest lower bound in a poset, 247 in an ordered field, 3 12, 3 18 of a set of real numbers, 221 of an infinite coll ...
INDEX 389 Interval(s), 7, 15, 160, 168 bounded, 8 closed, 8 continuous image of, 317 convexity of, 169, 200 intersection of, 161 ...
590 INDEX Logically implies, 69. See also Implication(s) Lower bound, 246,3 1 1 Lower triangular matrix, 169, 177 Mapping(s), 25 ...
INDEX 391 Numerical equivalence, 269, 288 of a set with its power set (invalidity of), 284 of N with Q, 281 of N with (0, 1) [in ...
392 INDEX Predicate(s) (continued) logical equivalence between, 83,94 logical implication between, 94 Premise of a conditional s ...
INDEX 393 partial ordering, 227,245 range of, 233 reflexive, 232 static view of, 231 subset, 232,246 symmetric, 232 transitive, ...
394 INDEX Statement (continued) simple, 55 truth value of, 54 Statement form(s), 56 biconditional, 61 component of, 56 condition ...
INDEX 395 Triangle inequality, 153, 157 generalized, 186 in an ordered field, 307 Trichotomy, 304,340 Trigonometric functions, 2 ...
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