From f61026119df4700f69eb73e95620bc5928ca0fcb Mon Sep 17 00:00:00 2001 From: User Date: Tue, 13 Oct 2009 02:52:09 +0000 Subject: Grand rename for gitit transfer --- math/algebra.page | 79 +++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 79 insertions(+) create mode 100644 math/algebra.page (limited to 'math/algebra.page') diff --git a/math/algebra.page b/math/algebra.page new file mode 100644 index 0000000..3e39ddb --- /dev/null +++ b/math/algebra.page @@ -0,0 +1,79 @@ +==================== +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:$\frac{a}{b}$ + - :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. -- cgit v1.2.3