To paraphrase Albert Einstein, a number in and by itself has no significance and only deserves the designation of number by virtue of its being a member of a group of objects with some shared characteristics. The most common characteristic of numbers is that they can be added and multiplied to produce other numbers in their group. However, not all objects that can be added or multiplied are designated as numbers.

As a matter of fact, there are many different kinds of numbers.

- rational and irrational
- real and complex
- imaginary
- algebraic and transcendental
- perfect
- surreal
- hyperreal numbers
- square and triangular numbers