394 INDEX
Statement (continued)
simple, 55
truth value of, 54
Statement form(s), 56
biconditional, 61
component of, 56
conditional, 61
contingency, 59,63
contradiction, 59
logically equivalent, 60
stronger, 69, 74, 97, 104, 108
tautology, 59
weaker, 69
Static view
of a function, 254
of a relation, 231
Story problems, 29
Stronger statement form, 69, 74,97, 104,
108
Subfield, 296, 359
Subset, 11,15, 116,160,211,231
proper, 12, 15, 165, 169
Subset relation, 232, 246
reflexive property of, 11,40
transitive property of, 11,40, 118
Substitution, 82
Subtraction
closure under, 347
in a field, 301
in N, 339
invalidity of associative property, 154
Successor function, 331
Sufficient, 72
Summation
closed form of, 181
formulas, 181,186
induction proofs involving, 18 1
notation, 181
properties, 188
Superset, 11
Supremum, 247
Surjection, 266, 273. See also Surjective
mapping
Surjective mapping, 266, 267, 271, 273
Syllogism, see Law of Syllogism
Sylow theorem (third), 223
Symmetric
in definition of equivalence relation, 236
matrix, 158,200
property of a relation, 232
property of set equality, 1440
Symmetric difference, 20
associative property of, 41, 158
commutative property of, 41
Symmetry
negation of definition of, 164
with respect to the origin, 99, 160, 168,
208
with respect to the x axis, 99, 160, 165,
168,208
with respect to the y axis, 160, 165, 166,
168,208
with respect to an arbitrary point, 168
Tautology(ies), 59, 63
lists of, 68-69, 70
with the conditional as main connective,
see Implication(s)
with the biconditional as main
connective, see Equivalence(s)
Theorem(s), 40, 149, 298
binomial, 188
Cantor's, 284
classification, 222
deMoivre's, 324, 326
extreme value, 318
Heine-Borel, 223, 3 18
intermediate value, 315
involving a conditional, 36
Lagrange's, 42,223
mean value, 24,222
of set theory, 39-42
of the predicate calculus, 95-101, 104,
106,107
of the propositional calculus, 64-76
Rolle's, 221
sandwich, 202
Schroeder-Bernstein, 276, 285, 289
third Sylow, 223
Tychonoff, 224
Topology, 100, 191
Totally ordered set, 248
Tracing ancestry, 276,286
Transcendental function, 254
Transfinite induction, 224
Transfinite processes, 224
Transitive
in definition of equivalence relation,
236
in definition of partial ordering, 245
property of a relation, 232
property of set equality, 10,40, 21 1
property of the subset relation, 11, 40,
118
Translation into English
of connectives, 72
of statements involving quantifiers, 89
Transpose of a matrix, 158
Tree diagram, 44