- 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

## Additional concepts

- Sets and set notation
- Hardware multiplication circuit
- Divide by zero