Mathematic Glossary - A to H

SN

A to H

1

Abel's Limit Theorem

2

Abel's test for series

3

Abel, Niels (1802-1829)

4

Abel’s theorem on power series

5

absolute convergence implies converges

6

absolute convergence of series

7

accumulation points

8

accumulation points and bounded sets

9

accumulation points and isolated points

10

aleph null

11

almost everywhere convergence

12

alternating harmonic series

13

alternating series

14

alternating series test

15

antiderivative

16

antiderivatives of standard functions

17

approximating function by derivative

18

Archimedes (287?-212 B.C.)

19

Archimedien Property

20

Barber of Seville

21

Bernoulli's inequality

22

Bernoulli, Johann (1667-1748)

23

bijection

24

binomial sequence

25

binomial series

26

binomial theorem

27

Bolzano's theorem

28

Bolzano, Bernard (1781-1848)

29

Bolzano-Weierstrass theorem

30

boundary and closed sets

31

boundary and interior

32

boundary points

33

bounded above

34

bounded below

35

bounded measurable functions, integrable

36

bounded sequences

37

bounded sequences and convergence

38

bounded sets and accumulation points

39

Cantor function

40

Cantor set

41

Cantor, Georg (1845-1918)

42

Cantor-Bernstein theorem

43

cardinality

44

cardinality of continuum

45

cardinality of power set

46

Cauchy condensation test for series

47

Cauchy criteria

48

Cauchy criterion for series

49

Cauchy product

50

Cauchy sequence

51

Cauchy sequence and convergence

52

Cauchy, Augustin (1789-1857)

53

center of convergence, power series

54

chain rule

55

characteristic function

56

closed

57

closed set, inverse image under continuous function

58

closed sets and boundary

59

closed sets and sequences

60

closed sets, intersections of

61

closed sets, unions of

62

compact

63

compact means closed and bounded

64

compact set, image under continuous function

65

compact sets, nested

66

comparison test for series

67

complement

68

completeness of R

69

conditional convergence and rearrangement

70

conditional convergence of series

71

connected

72

connected set, image under continuous function

73

connected sets in R

74

continuity and inverse images

75

continuity and limits

76

continuity and uniform convergence

77

continuity, uniform

78

continuous

79

continuous and differentiable

80

continuous and uniformly continuous

81

continuous functions on compact set

82

continuum hypothesis

83

contradiction, proof by

84

convergence almost everywhere

85

convergence, absolute

86

convergence, conditional

87

convergence, pointwise

88

convergence, uniform

89

convergent sequence

90

convergent sequences and subsequences

91

convergent sequences are bounded

92

convergent series

93

cos function, definition via Taylor series

94

countability of rationals

95

countable

96

countable hotel rooms

97

countable unions

98

cover

99

De Morgan's laws

100

De Morgan, Augustus (1806-1871)

101

decreasing function

102

Dedekind Cuts

103

Dedekind's Theorem

104

density principle

105

derivative of function

106

derivative, linear approximation

107

derivatives, monotonicity, and local extrema

108

differentiability and uniform convergence

109

differentiable and continuous

110

differentiable function

111

differential, total

112

differentiating power series

113

disconnected

114

disconnected, totally

115

discontinuities of monotone functions

116

discontinuity of first kind

117

discontinuity of second kind

118

discontinuity, classification

119

discontinuity, removable

120

discontinuous

121

disjoint

122

distributive law for sets

123

divergence test for series

124

divergent sequence

125

divergent series

126

division of Taylor series

127

domain

128

e (Euler's number)

129

e (Euler's number) is irrational

130

enumeration

131

equality of sets

132

equivalence class

133

equivalence relation

134

essential discontinuity

135

Euclid (330?-275? B.C.)

136

Euclid's theorem

137

Euler's number

138

Euler's number is irrational

139

Euler's sequence

140

Euler's series

141

Euler, Leonhard (1707-1783)

142

exponent sequence

143

exponential function, definition via Taylor series

144

exponential sequence

145

extremum

146

family of functions

147

Fibonacci numbers

148

finite cross products

149

first derivative test

150

function

151

function family

152

function sequence

153

function series

154

fundamental theorem of calculus

155

fundamental theorem of calculus, first

156

fundamental theorem of calculus, second

157

geometric series

158

Goedel and continuum hypothesis

159

greatest lower bound

160

harmonic series

161

harmonic series and the Leaning Tower of Lire

162

Heine-Borel theorem

163

Hilbert’s Hotel