Is there a number system other than real numbers?

Answer 1

There are several that are especially important:

• integers: ..., -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...
• rational numbers: ie, numbers that can be written as quotients of integers, such as 1/2, 7/8, etc.
• Irrational Numbers: ie, numbers that cannot be written as quotients of integers, pi, for example
• complex numbers: consisting of a pair of real numbers, and different arithmetic
• numbers 'modulo' a prime, similar to clock arithmetic, where, for instance, 5+9=2 modulo 12.

Some of these are subsets of the reals, others aren't.