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diff --git a/math/algebra b/math/algebra new file mode 100644 index 0000000..b337a2e --- /dev/null +++ b/math/algebra @@ -0,0 +1,71 @@ +==================== +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. |