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====================
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:`$\frac{a}{b}$`
- :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.
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