INDEX 385of composition (invalidity of), 261
of conjunction, 68
of disjunction, 68
of intersection, 32,40, 123
of multiplication, 15, 295, 338, 343
of symmetric difference, 41
of union, 32,40, 123
Commutative ring, 346
Compact
set, 211, 223
subset of a metric space, 99
Comparable
cardinal numbers, 288
elements in a poset, 249
Complement of a set, 18, 25, 100, 175, 214,
219
relative, 19, 219
Complete ordered field, 294, 296, 313, 359
Complex conjugate, 14, 322
Complex exponential, 325
Complex number(s), 7, 296, 319-328
argument of, 324
complex conjugate of, 14, 322
equality of, 320
field of, 296, 321
imaginary part of, 14, 321
modulus of, 14, 322
non-orderability of, 54, 304-305
nth root of, 326
polar form, 324
product of, 320
real part of, 14, 321
sum of, 320
Component of a statement form, 56
Composite of functions, 260
Composition
associativity of, 262
left cancellation property of, 263, 268
noncommutativity of, 261
of functions, 252, 258, 260
of mappings, 258, 262
right cancellation property of, 266, 267,
268
Compound statement, 52, 53, 55
Conclusion
error of assuming, 163
of a conditional statement form, 61
of an argument, 76
Conditional, 53
between predicates, 85
connective, 61
English language translation of the, 72
theorems involving, 35
weaker than the biconditional, 70
Conditional statement form
conclusion of, 61
contrapositive of, 65, 73
converse of, 65, 73
inverse of, 65, 73
premise of, 61
Congruence modulo, 232,237,239
equivalence classes generated by, 243, 244
Congruent triangles, 148,227,240
Conjecture, 23, 30-36
disproving, 154, 164
methods of arriving at, 23-24
Conjunction, 56
commutative property of, 68
associative property of, 68
between predicates, 85
Connective, 53. See also Logical
connective(s)
Constant function, 255
Construction of the reals, 352-361
Contingency, 59,63
Continuous
at a point, 74, 129
left, 144
on an open interval, 144
right, 144
uniformly, 144, 223
Continuum
cardinal number of the, 283
hypothesis, 287
Contradiction, 59, 63
proof by, 121,204,209,210
Contrapositive, 65, 73
proof by, 67,204,205
Convergent sequence, 191, 203, 353
Converse, 65, 73
partial, 175
Convex set, 169,200,211
Coordinate system, 22-23
Coplanar lines, 240
Corollary, 70
Countable intersection, 125, 290
Countable set, 283
Countable union, 125, 290
Countably infinite collection of sets, 127,290
Countably infinite set, 281, 283, 289
Counterexample, 154, 164
Counting arguments, 42,223
Counting properties of sets, 42-51
Critique and complete, 124, 159, 169, 177,
188
Cross product of sets, 22. See also
Cartesian product
Cyclic group, 75, 99