Infinite set

[1] The set of natural numbers (whose existence is postulated by the axiom of infinity) is infinite.

Important ideas discussed by David Burton in his book The History of Mathematics: An Introduction include how to define "elements" or parts of a set, how to define unique elements in the set, and how to prove infinity.

[5] Burton also discusses proofs for different types of infinity, including countable and uncountable sets.

[8] Burton also discusses proofs of infinite sets including ideas such as unions and subsets.

[5] In Chapter 12 of The History of Mathematics: An Introduction, Burton emphasizes how mathematicians such as Zermelo, Dedekind, Galileo, Kronecker, Cantor, and Bolzano investigated and influenced infinite set theory.

Many of these mathematicians either debated infinity or otherwise added to the ideas of infinite sets.

Potential historical influences, such as how Prussia's history in the 1800s, resulted in an increase in scholarly mathematical knowledge, including Cantor's theory of infinite sets.