A number is the symbolic representation of quantity. Humans represent numbers using the bae 10 numeric system. Mathematicians formally represent numbers as sets: set of natural numbers, set of integers, set of real numbers, and so on.

The first tool that numbers are used for is to count how many of something there is. This set of numbers is called the set of natural numbers and is associated with the subject of discrete mathematics.

The basic operations associating with the set of natural numbers are addition, subtraction, multiplication, and division. These form the basis of elementary mathematics.

Addition is a basic operation in mathematics for combining two numbers together. It is a binary operation denoted with the plus symbol with an expression on the left and an expression on the right.

Subraction is a basic arithmetic operation of taking away one number from another number.

Multiplication is a basic arithmetic operation performed on two numbers. Multiplying a number by another number is the same as taking n groups of the other number.

The division operator returns the result of dividing one number by another number.

Updating the properties of operations…

The functionality of a number is extended beyond the scope of the natural numbers by adding the notion of fractions and the syntax of the decimal point.

The decimal point is used to separate the whole part of a number from the decimal part. The whole part is represented using number digits to the left of the decimal point. The decimal part is also represented using digits to the right of the decimal point.

A fraction is represented using a horizontal bar between two expressions. The expression on top is called the numerator and the expression on bottom is called the denominator.

Scientific notation is a notation that scientists use to keep track of the number of significant digits in a number as well as easily recognize the magnitude of a number.

Updating the properties of operations…

A prime number is a number that is only divisible by itself and one. The set of prime numbers is infinitely big. The first prime numbers are 2, 3, 5, 7, 11, ... and continues on forever.

The set of natural numbers, also called the counting numbers, contains the numbers 0, 1, 2, 3, ...

The set of real numbers contains the set of rational numbers as well as irrational numbers like pi, e, and the square root of two.