INDEX 389Interval(s), 7, 15, 160, 168
bounded, 8
closed, 8
continuous image of, 317
convexity of, 169, 200
intersection of, 161, 168
nested, 125
open, 8
unbounded, 8
union of, 168, 177
Into mapping, 266
Intuitionist school, 219
Inverse
additive, 104,220,295,346,350
image of a set under a function, 252,
270-275
multiplicative, 220, 296, 338, 350
of a conditional statement form, 65, 73
of a function, 252, 258
of a mapping, 269,274
of a matrix, 200, 220
of a relation, 233
trigonometric functions, 159
Invertible
function, 259
matrix, 191, 193,200,220
Irrational number, 110,21 1,212,353
Irreflexive relation, 309
Isomorphism, 346
Join of two elements in a poset, 249, 250
Lagrange's theorem, 42,223
Law of
addition, 70
detachment, 70
disjunction, 70
double complementation, 40, 123
simplification, 70
syllogism, 70, 75
Least element
in a poset, 247
of a subset of N, 340
Least upper bound
axiom, 218, 221
in a poset, 247
in an ordered field, 312
of a set of real numbers, 215,3 1 1
of an infinite collection of sets, 128
Ldt cancellation property of composition,
263,268
Lef't continuous, 144
Left-hand limit, 143, 202, 203
Lcibniz, Gottfried Wilhelm von, 132
Lemma, 70
Tukey's, 224
Zorn's, 224
Less than
between cardinal numbers, 284
in an ordered field, 305
on R, 232
Less than or equal to
as a relation, 231, 245, 246
between cardinal numbers, 284
in an ordered field, 306
on R, 231
Limit
at infinity, 144
epsilondelta definition of, 52, 1 15, 132
infinite, 131
left-hand, 143, 202, 203
of a function, 52, 1 15, 128, 145, 186
of a sequence, 191,203
one-sided, 131,202
right-hand, 143,202,203
types I, 11,111, 129-132
uniqueness of, 21 3, 21 5, 220
Linear algebra, 100, 146, 161
Liliear function, 254
Linearly dependent set of vectors, 165,212
Linearly independent set of vectors, 161
Linearly ordered set, 248
Logarithm function, 258
Logic, 52-1 14
Logical argument, 76
conclusion of, 76
partial premise of, 76
premise of, 76
Logical connective(s), 55
alternation, 56
biconditional, 61
conditional, 53, 61
conjunction, 56
denial, 56
disjunction, 56
in predicates, 84-85
translation into English of, 72
Logical equivalence
between predicates, 83,94
of statement forms, 60
proving, 166
statement of, 42
Logical implication
between predicates, 94
between statement forms, 69
statement of, 42
Logically equivalent, 60.