To infinity and beyond book pdf

Since pre-Socratic times, philosophers have speculated about the nature of the infinite. For example, Zeno of Elea proposed many paradoxes involving infinity, and Eudoxus of Cnidus used the idea of indefinitely small quantities in his method of exhaustion , though the notion of passing to the limit—which lies at the basis of the infinitesimal calculus —was never formulated in ancient Greece. At the end of 19th century, Georg Cantor introduced and studied infinite sets and infinite numbers , [2] which are now an essential part of the foundations of mathematics through [ clarification needed ] Zermelo—Fraenkel set theory. For example, in modern mathematics, a line is commonly viewed as the set of all of its points, and their infinite number the cardinality of the line is larger than the number of integers. The mathematical concept of infinity and the manipulation of infinite sets are used everywhere in mathematics, even in areas such as combinatorics that may seem to have nothing to do with them. For example, Wiles's proof of Fermat's Last Theorem uses the existence of very large infinite sets.

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Eli Maor examines the role of infinity in mathematics and geometry and its cultural impact on the arts and sciences.
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