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diff --git a/math/algebra.page b/math/algebra.page index e1a44db..658267e 100644 --- a/math/algebra.page +++ b/math/algebra.page @@ -1,85 +1,42 @@ --- -format: rst +format: markdown categories: math toc: no ... -==================== -Algebra -==================== +# Algebra -.. note:: Most of the definitions and notation in the section are based on [rudin]_ or [meserve]_ +*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 +Name Symbol Pos. Integers? Pos. Rationals? Rationals? Reals (wrt Pos Int.)? Complex? +---- ----------------- -------------- --------------- ---------- --------------------- -------- +addition $a + b$ Y Y Y Y Y +product $a\times b$ Y Y Y Y Y +subtraction $a-b$ N N Y Y Y +division $\frac{a}{b}$ N Y Y Y Y +power $a^b$ Y Y Y Y Y +root $\sqrt{\text{a}}$ N N N Y Y +---- ----------------- -------------- --------------- ---------- --------------------- -------- - * - 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 +Table: Closure of binary operators on given sets of numbers -Definitions -============= +## Definitions -*involution* +involution to raise a number to a given power -*evolution* +evolution to take a given root of a number -*associative* - :latex:`$(a+b)+c=a+(b+c)$` +associative + $(a+b)+c=a+(b+c)$ -*comutative* - :latex:`$a+b=b+c$` +comutative + $a+b=b+c$ -*distributive* - :latex:`$(a+b)c=ac+bc$` +distributive + $(a+b)c=ac+bc$ -.. [rudin] `Principles of Mathematical Analysis (3rd ed)`:title:, by Walter Rudin. McGraw-Hill, 1976 +[^rudin] **Principles of Mathematical Analysis (3rd ed)**, by Walter Rudin. McGraw-Hill, 1976 -.. [meserve] `Fundamental Concepts of Algebra`:title:, by Bruce Meserve. +[^meserve] **Fundamental Concepts of Algebra**, by Bruce Meserve. |