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The concept of infinity has a long and somewhat controversial history in mathematics. It was first formally introduced by the ancient Greek mathematician Zeno of Elea in the 5th century BCE, although the idea of infinitely large and small quantities had been discussed by earlier philosophers such as Aristotle.

One of the main reasons for introducing the concept of infinity was to deal with certain paradoxes that arose in the study of motion and change. For example, Zeno's paradoxes of motion, such as the Dichotomy Paradox, suggest that it is impossible for an object to move from one place to another because it must first traverse an infinite number of points in order to do so. The concept of infinity allows us to resolve these paradoxes by stating that there are indeed infinite quantities, and that it is possible for an object to pass through an infinite number of points in a finite amount of time.

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