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* The [[ordinal sum|sum]], [[ordinal product|product]], or [[ordinal exponentiation|exponentiation]] of an infinite ordinal with any other ordinal is infinite, except in the case of multiplying or exponentiating by [[0]], and exponentiation with base 0 or [[1]].
* The [[cardinal sum|sum]], [[cardinal product|product]], or [[cardinal exponentiation|exponentiation]] of an infinite cardinal with any other cardinal is infinite, with the same exceptions as above.
== Infinity ==
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, such as denoting certain [https://en.wikipedia.org/wiki/Limit_(mathematics)#Infinity_as_a_limit limits] or [https://en.wikipedia.org/wiki/Improper_integral improper integrals], or as an [https://en.wikipedia.org/wiki/Extended_real_number_line extended real number]. 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
\(x\) there is a natural at least as large, such as \(\lceil x\rceil\). Infinity should also not be conflated with infinite ordinals or cardinals such as \(\omega\) and \(\aleph_0\).
== External links ==
* {{Wikipedia|Infinite set}}▼
* {{Mathworld|Infinite Set}}
* {{Mathworld|Infinity}}
▲* {{Wikipedia|Infinite set}}
* {{Wikipedia|Infinity}}
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