Index
A complement, 100,175,214,219
Abelian group, 75,99
Absolute maximum and minimum, 157
Absolute value
in an ordered field, 307
of a real number, 156, 174
Abstract algebra, 42, 75, 100, 146, 224, 346
Accumulation point, see Point of
accumulation
Addition
associative property of, 15, 295, 336
cancellation property of, 299, 336, 342
closure property of, 212,295
commutative property of, 15,295, 336
in Q, 349
in R, 356
in Z, 344
law of, 70
of complex numbers, 320
of equivalence classes of Cauchy
sequences, 356
recursive definition of, 335
Additive identity, 104,219,295,336,346,350
Additive inverse, 104, 220, 295, 346, 350
Adequate set of connectives, 76
Advanced calculus, 146, 191
Advanced methods of proof, 190-224
Aleph-null, 283
Algebra
abstract, 42,75, 100, 146,224, 346
boolean, 53
elementary, 19 1
intermediate, 148, 149
linear, 100, 146, 161
of sets, 16, 29
Algebraic function, 254, 264
Algebraic operation, 15
binary, 16,294
preserving, 346
well-defined, 330, 344-345, 350, 358
Algebraic structure, 295
of integers modulo m, 297
of polynomials in one variable, 298, 360
of 2 x 2 matrices, 297
Alternation, 56. See also Disjunction
exclusive, 56, 59
Analysis of arguments, 76-80, 110-114
Ancestor, 276,286
Antisymmetric
in definition of partial ordering, 245
matrix, 158, 200
property of a relation, 232
Arbitrary collection of sets, 127,252,289,290
Arbitrary intersection, 290
Arbitrary union, 290
Archimedean
ordered field, 3 14, 359
property, 126,201,221
Argument@)
analysis of, 76-80, 110- 114
compactness, 223
counting, 42,223
logical, 76
valid, 76-80, 110- 114
Argument of a complex number, 324
principal value of, 324
Associative property
of addition, 15, 295, 336
of composition of functions, 262
of conjunction, 68
of disjunction, 68
of intersection, 32, 40, 123