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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
- :latex:`$+$`
- :latex:`$\times$`
- :latex:`$-$`
- :latex:`$\divide$`
- :latex:`$^$`
- :latex:`$\sqrt{\text{ }}$`
* 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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