• Mathematicians have classified all number-like objects into sets (i.e. Naturals, Integers, Rationals, Reals, Complex Numbers), which each encompass the preceding set. Naturals consist of counting numbers (e.g. 0, 1, 2, 3), while Integers also include negative numbers derived through subtraction. Rationals also includes quotients of integers, while Reals also consist of their irrational counterparts (i.e. numbers that cannot be expressed as a quotient of two integers, like the square-root of two).
• The three main operations on numbers include addition/subtraction, multiplication/division, and exponentiation/roots
• Both addition and subtraction can be represented by moving along the number line
• Addition and multiplication are both commutative and associative
• A positive integer in an exponent indicates repeated multiplication by one, while a negative in an exponent indicates the inverse operation, or repeated division by one
• When a number is multiplied by itself n times to equal another number, it is considered the nth root of the other number
• A fraction in an exponent means the inverse operation of division should be performed (e.g. square-root instead of a square)
• Operation precedence consists of first solving exponents/roots, then products/divisons, and finally additions and subtractions
• The basic rules of algebra include the associative, commutative, and distributive properties