Bridge to Abstract Mathematics: Mathematical Proof and Structures

INDEX 395

Triangle inequality, 153, 157
generalized, 186
in an ordered field, 307
Trichotomy, 304,340
Trigonometric functions, 258
inverse, 159
Trigonometric identities, 155, 176
Trigonometry, 150
Truth set, 82,83
Truth table, 56
proof by, 64
Truth value, 54
Tukey's lemma, 224
Tychonoff s theorem, 224
Type I, 11, I11 limits, 129-132, 142

Unbounded interval, 8

Uncountable set, 283

Undecidable proposition, 287

Uniformly continuous, 144, 223

Union, 16, 25

arbitrary, 290

associative property of, 32,40, 123

commutative property of, 32,40, 123

countable, 125, 290

idempotent property of, 40, 123

identity for, 40, 121

infinite, 125- 128

of intervals, 168, 177

Uniqueness, 100

of identities and inverses in a field, 299

of the limit, 213, 215,220

proofs of, 212,214-216,219-222

Universal quantifier, 88

Universal set, 6, 36-37

Unknown

in a predicate, 82

in a statement form, 56

Upper bound, 246,3 1 1

Upper triangular matrix, 99, 169, 177

Valid argument, 76-80, 110-1 14

Variable, 82

dependent, 254

dummy, 88, 125

in a predicate, 82, 88

independent, 254

Vector space, 161

Venn diagram(s), 24, 28, 30

in logic, 111-113

"proof by," 30, 36

use in counting, 49

Weaker statement form, 69

Weierstrass, Karl, 132

Well defined

operation, 330, 344-345, 350, 358

relation, 250

set, 4, 14

Well ordering principle, 187, 218, 221, 330,

340,341,343

Zorn's lemma, 224