In 1886 the mathematician Leopold Kronecker famously said, “God Himself made the whole numbers — everything else is the work of men.” Indeed, mathematicians have introduced new sets of numbers besides the ones used to count, and they have labored to understand their properties.
Although each type of number has its own fascinating and complicated history, today they are all so familiar that they are taught to schoolchildren. Integers are just the whole numbers, plus the negative whole numbers and zero. Rational numbers are those that can be expressed as a quotient of integers, such as $3, -\dfrac{1}{2}$ and $\dfrac{57}{22}$. Their decimal expansions either terminate $(-\dfrac{1}{2} = −0,5)$ or eventually repeat $(\dfrac{57}{22} = 2,509090909…)$. That means if a number has decimal digits that go on forever without repeating, it’s irrational. Together the rational and irrational numbers comprise the real numbers. Advanced students learn about the complex numbers, which are formed by combining the real numbers and imaginary numbers; for instance, $i=\sqrt{-1}$.
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