INDEX 391Numerical equivalence, 269, 288
of a set with its power set (invalidity of),
284
of N with Q, 281
of N with (0, 1) [invalidity of], 282
of R with the power set of N, 286
Odd
function, 157
integer, 59, 200, 211
One-sided limit, 131, 202
Oneto-one
correspondence, 252,269
function, 168, 208, 21 1, 252, 256
mapping, 257
Onto mapping, 252, 257, 266
Open
interval, 8
sentence, 53, 54, 82. See also Predicate
set, 191, 194, 201
Operation(s), 294
algebraic, 15
binary, 16, 294
on functions, 257
on sets, 15-23
Ordered by divisibility, 231, 250
Ordered by inclusion, 246
Ordered field, 294, 303, 304
absolute value in, 307
Archimedean, 314,359
completeness in, 309, 310, 359. See also
Complete ordered field
distance in, 308
greatest lower bound in, 312, 318
incomplete, 3 13
least upper bound in, 312
less than in, 305
less than or equal to in, 306
negative element of, 304
positive part of, 304
positive element of, 304, 358
triangle inequality in, 307
Ordered pair(s), 21, 123, 228
equality of, 21, 123,229
Ordering properties of the positive integers,
339-340
Ordering in Q, 351
Ordering in R, 358
Ordering in Z, 348
Pairwise disjoint, 125. See also Mutually
disj oh t
Parallel lines, 240
Parametrically described curve, 168
Partial converse, 175
Partially ordered set, 245
chain in, 248
greatest element of, 247
greatest lower bound in, 247
join of two elements in, 249, 250
least element of, 247
least upper bound in, 249,250
linearly ordered, 248
maximal element of, 250
meet of two elements in, 249, 250
minimal element of, 250
totally ordered, 248
Partial ordering, 227,245
Partial premise, 76
Partition, 240
cells of, 240
determined by an equivalence relation,
242
Pattern method, 6, 14, 253
Peano, Giuseppe, 329
Perpendicular lines, 101, 240
Permutation, 45
of n things taken n at a time, 46
of n things taken r at a time, 46
Pick-a-point method, 117. See also Choose
method
Pictures, 24
Pigeon-hole principle, 223
Pinching theorem, see Sandwich theorem
Plane geometry, 148
Point of accumulation, 201, 221
Polar coordinates, 169
Polar form of complex numbers, 324
Pol ynomial(s)
algebraic structure of, 298, 360
function, 254, 264
Poset, 245. See also Partially ordered set
Positive element in an ordered field, 304,
358
Positive integers, 7, 296, 330-343
ordering properties of, 339-340
Positive part of an ordered field, 304
Power set, 13, 168, 175
cardinality of, 286
number of elements in, 48, 187
Predicate calculus, 53, 8 1- 1 14
theorems of, 95-101, 104, 106, 107
Predicate+), 53, 82
containing logical connectives, 84-85
in one variable, 82
in several variables, 101