==================== 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:$\divide$ - :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.