blob: 5f15f4a015c17d8f5fbab7c21b83a4ff0d734f61 (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
|
====================
Algebra
====================
.. note:: Most of the definitions and notation in the section are based on [rudin]_ or [meserve]_
.. list-table:: Closure of binary operators on given sets of numbers
* - Operation name
- addition
- product
- subtraction
- division
- power
- root
* - Operation symbol
- :latex:`$a + b$`
- :latex:`$a\times b$`
- :latex:`$a-b$`
- :latex:`$\divide$`
- :latex:`$a^b$`
- :latex:`$\sqrt{\text{a}}$`
* - Positive Integers
- Y
- Y
- N
- N
- Y
- N
* - Positive rationals
- Y
- Y
- N
- Y
- Y
- N
* - Rationals (and zero)
- Y
- Y
- Y
- Y
- Y
- N
* - Reals wrt positive integers
- Y
- Y
- Y
- Y
- Y
- Y
* - Complex numbers
- Y
- Y
- Y
- Y
- Y
- Y
Definitions
=============
*involution*
to raise a number to a given power
*evolution*
to take a given root of a number
*associative*
:latex:`$(a+b)+c=a+(b+c)$`
*comutative*
:latex:`$a+b=b+c$`
*distributive*
:latex:`$(a+b)c=ac+bc$`
.. [rudin] `Principles of Mathematical Analysis (3rd ed)`:title:, by Walter Rudin. McGraw-Hill, 1976
.. [meserve] `Fundamental Concepts of Algebra`:title:, by Bruce Meserve.
|
