428
Index
least upper bound 56, 100, 216
limit
- algebraic operations 95
- infinite 138
- of a function on R or C 63, 187
- of a sequence 68
- of limits 239
- of series 241
- uniform 207,219,232,236,266,285
limit value of a function 187
local inversion theorem 290
local property 59
logarithm
- asymptotic behaviour 335
- and exponential function 107,195,
345
- definition and derivative 105,342
- functional equation 339
- of a complex number 377
- power series for log(l + x) 222,359
- to base a 332
majorant, majorised 100
map 19
- composed 23
- identity 25
- inverse 25
- linear tangent 274
mean - inequality of the mean 263
mean value theorem 261,263
- inequality of the mean 263
- inequality of the mean in the plane
282
membership relation 7
method of iteration 136
method of majorants 172
method of successive approximations
293
minorised 100
monotone (function) 197
- and differentiation 257
- inverse 202
- limit values 197
- piecewise 197
multiplication of series 167
Napierian logarithm 107
natural integers 14
negligible (function) 66
negligible with respect to 66
neighbourhood of a point 306
nested
- principle of nested intervals 225
norm (uniform) 217
normed (linear/vector space) 313
number
- 7r
375
- algebraic 46
- axioms of real numbers 54
- complex 50
- decimal expansion 28, 70
- rational integer 47
- real 45
- transcendental 46
of class C'P 252
order relation 34
ordered pair 17
ordered partial sums 77
orders of magnitude 61
- notations 0, 0 62,66
partial derivatives 273
partition
- of a number 408
- of a set 23
piecewise monotone function 197
point
- boundary 190
- exterior 188,306
- interior 189
- isolated 160
pole 179
power of the continuum 28
powers
- complex 350
- divided x[n) = xn In! 55
- index laws 331
- rational 325
- real 327
primitive (power series) 151
principle of nested intervals 225
proof by induction 16
property
- local 59
- true on a neighbourhood of a point
59,290
quantifiers, logical symbols 39
radius of convergence 126
rational exponents 325
real number 49
real-analytic (function) 161
roots
- of a complex number 382
Index
least upper bound 56, 100, 216
limit
- algebraic operations 95
- infinite 138
- of a function on R or C 63, 187
- of a sequence 68
- of limits 239
- of series 241
- uniform 207,219,232,236,266,285
limit value of a function 187
local inversion theorem 290
local property 59
logarithm
- asymptotic behaviour 335
- and exponential function 107,195,
345
- definition and derivative 105,342
- functional equation 339
- of a complex number 377
- power series for log(l + x) 222,359
- to base a 332
majorant, majorised 100
map 19
- composed 23
- identity 25
- inverse 25
- linear tangent 274
mean - inequality of the mean 263
mean value theorem 261,263
- inequality of the mean 263
- inequality of the mean in the plane
282
membership relation 7
method of iteration 136
method of majorants 172
method of successive approximations
293
minorised 100
monotone (function) 197
- and differentiation 257
- inverse 202
- limit values 197
- piecewise 197
multiplication of series 167
Napierian logarithm 107
natural integers 14
negligible (function) 66
negligible with respect to 66
neighbourhood of a point 306
nested
- principle of nested intervals 225
norm (uniform) 217
normed (linear/vector space) 313
number
- 7r
375
- algebraic 46
- axioms of real numbers 54
- complex 50
- decimal expansion 28, 70
- rational integer 47
- real 45
- transcendental 46
of class C'P 252
order relation 34
ordered pair 17
ordered partial sums 77
orders of magnitude 61
- notations 0, 0 62,66
partial derivatives 273
partition
- of a number 408
- of a set 23
piecewise monotone function 197
point
- boundary 190
- exterior 188,306
- interior 189
- isolated 160
pole 179
power of the continuum 28
powers
- complex 350
- divided x[n) = xn In! 55
- index laws 331
- rational 325
- real 327
primitive (power series) 151
principle of nested intervals 225
proof by induction 16
property
- local 59
- true on a neighbourhood of a point
59,290
quantifiers, logical symbols 39
radius of convergence 126
rational exponents 325
real number 49
real-analytic (function) 161
roots
- of a complex number 382