What are two subsets of real numbers that are mutually exclusive?

Take any set; this set and its complement are mutually exclusive. Here are some examples:

• Negative and non-negative (i.e., positive and zero) numbers
• Rational and Irrational Numbers
• Integers and non-integers
• Algebraic and transcendental numbers

You can also take a set and its complement from a smaller universe; these would also be mutually exclusive. For example:

• Even and odd numbers (only includes integers)