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diff --git a/math/algebra.page b/math/algebra.page index 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. |