Editing Number (section)

===Infinity and infinitesimals {{anchor|History of infinity and infinitesimals}}===
{{further|History of infinity}}
The earliest known conception of mathematical [[infinity]] appears in the [[Yajur Veda]], an ancient Indian script, which at one point states, "If you remove a part from infinity or add a part to infinity, still what remains is infinity." Infinity was a popular topic of philosophical study among the [[Jain]] mathematicians c. 400&nbsp;BC. They distinguished between five types of infinity: infinite in one and two directions, infinite in area, infinite everywhere, and infinite perpetually. The symbol <math>\text{∞}</math> is often used to represent an infinite quantity.

[[Aristotle]] defined the traditional Western notion of mathematical infinity. He distinguished between [[actual infinity]] and [[potential infinity]]—the general consensus being that only the latter had true value. [[Galileo Galilei]]'s ''[[Two New Sciences]]'' discussed the idea of [[bijection|one-to-one correspondences]] between infinite sets. But the next major advance in the theory was made by [[Georg Cantor]]; in 1895 he published a book about his new [[set theory]], introducing, among other things, [[transfinite number]]s and formulating the [[continuum hypothesis]].

In the 1960s, [[Abraham Robinson]] showed how infinitely large and infinitesimal numbers can be rigorously defined and used to develop the field of nonstandard analysis. The system of [[hyperreal numbers]] represents a rigorous method of treating the ideas about [[infinity|infinite]] and [[infinitesimal]] numbers that had been used casually by mathematicians, scientists, and engineers ever since the invention of [[infinitesimal calculus]] by [[Isaac Newton|Newton]] and [[Gottfried Leibniz|Leibniz]].

A modern geometrical version of infinity is given by [[projective geometry]], which introduces "ideal points at infinity", one for each spatial direction. Each family of parallel lines in a given direction is postulated to converge to the corresponding ideal point. This is closely related to the idea of vanishing points in [[perspective (graphical)|perspective]] drawing.