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 diff --git a/math/algebra.page b/math/algebra.pageindex 658267e..27edb31 100644--- a/math/algebra.page+++ b/math/algebra.page@@ -6,37 +6,43 @@ toc: no # 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].* +----------- ----------------- -------------- --------------- ---------- --------------------- -------- 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----- ----------------- -------------- --------------- ---------- --------------------- --------+----------- ----------------- -------------- --------------- ---------- --------------------- -------- Table: Closure of binary operators on given sets of numbers ## Definitions involution- to raise a number to a given power+: to raise a number to a given power evolution- to take a given root of a number+: to take a given root of a number associative- $(a+b)+c=a+(b+c)$+: $(a+b)+c=a+(b+c)$ -comutative- $a+b=b+c$+commutative+: $a+b=b+c$ distributive- $(a+b)c=ac+bc$+: $(a+b)c=ac+bc$ -[^rudin] **Principles of Mathematical Analysis (3rd ed)**, by Walter Rudin. McGraw-Hill, 1976+[^rudin]: **Principles of Mathematical Analysis (3rd ed)**, by Walter Rudin. McGraw-Hill, 1976 -[^meserve] **Fundamental Concepts of Algebra**, by Bruce Meserve.+[^meserve]: **Fundamental Concepts of Algebra**, by Bruce Meserve.