Not Complex Numbers: Are There Any Other Options?

[Mathsforum100]

Are there any numbers in mathematics that are not complex numbers?

 

[Reptillian]

Quaternions?

 

[micromass]

There are no such things as "numbers" in mathematics. It is a term that is used and abused a lot. We have

- Rational numbers
- Real numbers
- Complex numbers
- p-adic numbers
- Transfinite numbers
- Hyperreal numbers
- Surreal numbers
- Supernatural numbers
- etc.

Some of these things are not what you have in mind when you talk about numbers, but they're called numbers anyway. The term numbers is overloaded and doesn't have any real meaning: there is no definition to determine whether something is a number or not.