# Algebra

Note: Most of the definitions and notation in the section are based on 1 or 2.

Closure of binary operators on given sets of numbers
Name Symbol Pos. Integers? Pos. Rationals? Rationals? Reals (wrt Pos Int.)? Complex?
addition a + b Y Y Y Y Y
product a × b Y Y Y Y Y
subtraction a − b N N Y Y Y
division $\frac{a}{b}$ N Y Y Y Y
power ab Y Y Y Y Y
root $\sqrt{\text{a}}$ N N N Y Y

## Definitions

involution
to raise a number to a given power
evolution
to take a given root of a number
associative
(a + b) + c = a + (b + c)
commutative
a + b = b + c
distributive
(a + b)c = ac + bc

1. Principles of Mathematical Analysis (3rd ed), by Walter Rudin. McGraw-Hill, 1976↩︎

2. Fundamental Concepts of Algebra, by Bruce Meserve.↩︎