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Cohen L.W., Ehrlich G. — The Structure of the Real Number System
Cohen L.W., Ehrlich G. — The Structure of the Real Number System



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Название: The Structure of the Real Number System

Авторы: Cohen L.W., Ehrlich G.

Аннотация:

The present course of mathematical education in school and college introduces a student rather casually to the various properties of integers, rational numbers, and real numbers as they are needed for arithmetic, algebra, geometry, and calculus. Sometimes the relations among these mathematical structures are sketched as indications of things to come in mathematics. When the student begins graduate study he finds that he is expected to be familiar with the structure of the real number HyHtem. If his graduate courses deal explicitly with this system at all, they usually do so in terms of a brief summary. It is then assumed that the student has a usable knowledge of the intricately interwoven properties of set theory, algebra and topology which characterize the Hystcm of real numbers. Actually, this assumption is frequently false and a gap is left in the student's knowledge which, if not filled, hinders his development.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1963

Количество страниц: 124

Добавлена в каталог: 30.07.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute value      68
Accumulation point      94
Addition of integers      45
Addition of natural numbers      21
Addition of rational numbers      62
Addition of real numbers      82
Anti-symmetric      9
Archimedean order      69
Associative      15
Binary operation      15
Binary relation      9
Bounded sequence      73
Cartesian product      8 42
Categoricity      58 101
Choice, axiom of      35
Closed set      94
Co-domain      11
Commutative      15
Complete metric space      90 111
Complete ordered field      85
Complex number      106
Composition of mappings      13
Congruence      10
Convergence in metric spaces      90
Convergence in ordered fields      74
Couple      41
Covering      95
Cut      71
Dense order      69
Denumerable      37
DIMENSION      109
Disjoint sets      6
Distributive      15
Domain      11
Element of a set      2
Embedding      56 57 66 84
Empty set      4
Equivalence class      10
Equivalence relation      9 43 60 80 106
Existence, Axiom of      2
Factor set      11
Field      64
Finite set      34
first element      28
Function      11
Fundamental sequence in a metric space      89
Fundamental sequence in an ordered field      73
Gap      71
Generalized associative law      30
Generalized commutative law      32
Generalized Recursion Theorem      19
Greatest lower bound      93
Groupoid      24
I-product      42
I-tuple      41
Identity element      25
Identity, Axiom of      2
Index set      41
Induction, axiom of      16 17
Induction, Second Principle of      29
Inductive set      17
Infinite set      37
Initial segment      29
INTEGER      44
Integral domain      53
Intersection of sets      5
interval      93
Inverse element      46
Inverse mapping      13
Isometry      91
Isomorphism      56
Laurent series      70 101
Least upper bound      93
LIMIT      74
Lower bound      92
Mapping      11
Metric      89 110
Metric space      88 110
Multiplication of integers      49
Multiplication of natural numbers      23
Multiplication of rational numbers      62
Multiplication of real numbers      82
n-tuple      41
Natural number      16
Order for integers      52
Order for natural numbers      27
Order for rational numbers      66
Order for real numbers      84
Order relation      11
Ordered field      66
Ordered integral domain      53
Ordered pair      7
Ordered set      11
pair      5
Pairs, Axiom of      5
Partial order relation      11
Positive integer      51
Positive rational number      65
Positive real number      83
Positive sequence      77
Power set      6
Powers, Axiom of      6
Proper subset      3
RANGE      11
Rational number      61
Real number      81
Recursion theorem      18
Reflexive      9
Restriction of a binary operation      15
Restriction of a mapping      15
Ring      50
Semigroup      25
Set      2
Singleton      5
Specification, Axiom of      3
Subset      3
Successor      16
symmetric      9
Terminal segment      34
Transitive      9
Trichotomy      9
Union of sets      4
Unions, Axiom of      4
Upper bound      92
Vector space      108
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