- of unity 382
- positive pth root 108
Russell's Paradox 11
sequence 67
- (1 + xln)n 103,368
- n(xl/n - 1) 74
- nl/n 76
- xl/n 73
- zn In! 72
- convergent in Rorin C 67
- in a metric space 308
- increasing, convergence criterion 99
- infinite limits 138
series
- cotx 164,269,402
- (1 + z)S for s an integer 156
- 1/(m 2 + n 2 )S 118,142
- 10g(1 + x) 222,359
- absolutely convergent 123
- alternating 120
- alternating harmonic 119
- binomial 135,351
- comparison principles 132
- convergence criteria of Dirichlet,
Abel 235
- convergent 77
- convergent power 126
- criteria of Cauchy and d' Alembert
132
- decimal expansion as series 77
- derivative of a power series 150
- derivative, primitive of a power series
148
- Eisenstein, Weierstrass 179
- exponential 103,124
- formal 175
- geometric 78
- harmonic 82
- in a Banach space 313
- Laurent 168
- multiple 118,142
- multiplication of series 144, 167
- normally convergent 220
- ordered partial sums 77
- power 80,126
- primitive 151
- Riemann 163,221,222,268,395
- semi-convergent 123
- simple 77
- unconditionally convergent 127
-- associativity 140
- with positive terms 114
Index
429
set 7
- adherent, interior, exterior, boundary
(point) 187
- bounded 100
- cardinal number of a set 30
- complement 11
- countable 26
- defined by a relation 10
- disjoint sets 12
- empty 8
- equipotent sets 25
- finite 25
- finite, infinite 26
- inductive 16
- infinite 25
- intersection 12, 22
- of definition 20
- of values 20
- of whole numbers N 16
- open, closed 189,306
- ordinal, well ordered 31
- power of a set 26
- quotient 19
- set of subsets of a set 17
- subset (of a set) 8
- union 12, 22
sin x for x complex 373
space
- Banach 313
- Cartesian 303
- compact 320
- complete 308
- metric 304
- normed linear 313
- normed vector 313
- pre-Hilbert, Hilbert 314
- precompact 321
- topological 322
square wave 196,212,223
- uniform convergence 238
strictly increasing 197
surjection 24
surjective 24
symbols +00 and -00 58
tables of logarithms 73
tangent (linear map)
- of a function of one variable 245
- of a function of two variables 274
theorem
- Bolzano's Theorem 201
- Weierstrass' approximation theorem
209
- positive pth root 108
Russell's Paradox 11
sequence 67
- (1 + xln)n 103,368
- n(xl/n - 1) 74
- nl/n 76
- xl/n 73
- zn In! 72
- convergent in Rorin C 67
- in a metric space 308
- increasing, convergence criterion 99
- infinite limits 138
series
- cotx 164,269,402
- (1 + z)S for s an integer 156
- 1/(m 2 + n 2 )S 118,142
- 10g(1 + x) 222,359
- absolutely convergent 123
- alternating 120
- alternating harmonic 119
- binomial 135,351
- comparison principles 132
- convergence criteria of Dirichlet,
Abel 235
- convergent 77
- convergent power 126
- criteria of Cauchy and d' Alembert
132
- decimal expansion as series 77
- derivative of a power series 150
- derivative, primitive of a power series
148
- Eisenstein, Weierstrass 179
- exponential 103,124
- formal 175
- geometric 78
- harmonic 82
- in a Banach space 313
- Laurent 168
- multiple 118,142
- multiplication of series 144, 167
- normally convergent 220
- ordered partial sums 77
- power 80,126
- primitive 151
- Riemann 163,221,222,268,395
- semi-convergent 123
- simple 77
- unconditionally convergent 127
-- associativity 140
- with positive terms 114
Index
429
set 7
- adherent, interior, exterior, boundary
(point) 187
- bounded 100
- cardinal number of a set 30
- complement 11
- countable 26
- defined by a relation 10
- disjoint sets 12
- empty 8
- equipotent sets 25
- finite 25
- finite, infinite 26
- inductive 16
- infinite 25
- intersection 12, 22
- of definition 20
- of values 20
- of whole numbers N 16
- open, closed 189,306
- ordinal, well ordered 31
- power of a set 26
- quotient 19
- set of subsets of a set 17
- subset (of a set) 8
- union 12, 22
sin x for x complex 373
space
- Banach 313
- Cartesian 303
- compact 320
- complete 308
- metric 304
- normed linear 313
- normed vector 313
- pre-Hilbert, Hilbert 314
- precompact 321
- topological 322
square wave 196,212,223
- uniform convergence 238
strictly increasing 197
surjection 24
surjective 24
symbols +00 and -00 58
tables of logarithms 73
tangent (linear map)
- of a function of one variable 245
- of a function of two variables 274
theorem
- Bolzano's Theorem 201
- Weierstrass' approximation theorem
209