A number is a fundamental concept in mathematics, representing quantities or values. Typically, numbers are represented using the decimal number system and are organized into different sets representing different types of numbers:

Natural Numbers: Also known as counting numbers, these include all positive integers starting from zero ().

Integers: These include natural numbers and their negatives .

Rational Numbers: These are any numbers that can be expressed as the quotient or fraction of two integers, with the denominator not equal to zero.

Real Numbers: These include all numbers that can be depicted on a number line, including rational numbers and irrational numbers (numbers that can’t be expressed as simple fractions, such as or ).

Complex Numbers: These include all numbers that can be expressed as , where and are real numbers and . The real part is , and is the imaginary part.

Quaternions: These are an extension of complex numbers that can be expressed as , where are real numbers and are the fundamental quaternion units which satisfy .
Each type of number has different uses depending on the context. Over time, as our understanding of numbers evolved, different types of numbers have been defined and organized into these types.