Infinite: Difference between revisions

A separate concept to that of an infinite set is that of infinity itself, denoted \(\infty\). This generally refers to an object that is larger than all natural numbers. It has different precise meanings in different contexts. It can be used purely notationally, such as when denoting certain [https://en.wikipedia.org/wiki/Limit_(mathematics)#Infinity_as_a_limit limits to infinity], or[https://en.wikipedia.org/wiki/Series_(mathematics) series], and [https://en.wikipedia.org/wiki/Improper_integral improper integrals], or as an object in a structure such as the [https://en.wikipedia.org/wiki/Extended_real_number_line extended real numbernumbers]. However, there is no real number that serves the purpose of infinity, since the real numbers have the [https://en.wikipedia.org/wiki/Archimedean_property Archimedean property], meaning that for every real number