Number systems (other)

Beyond natural numbers, integers, and rational numbers, mathematicians have defined other number systems to solve more problems. These include irrational numbers (numbers that cannot be written as a fraction, like $\sqrt{2}$ or $\pi$), real numbers (all rational and irrational numbers), and complex numbers (numbers with a real and an imaginary part, like $2 + 3i$).

Important properties

• Irrational numbers cannot be written as a ratio of integers.

• Real numbers include both rational and irrational numbers.

• Complex numbers have the form $a + bi$, where $i$ is the imaginary unit with $i^2 = -1$.

• Each new number system is built to solve problems that earlier systems could not.