{{dated prod|concern = April's fool joke; Mathworld has lots of sillyness but we don't need it here|month = April|day = 2|year = 2009|time = 02:54|timestamp = 20090402025452}}
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In mathematics, the '''frivolous theorem of arithmetic''' is a tongue-in-cheek theorem which states that ''almost all natural numbers are very, very large''. This statement, although seemingly trivial, encapsulates many fundamental properties of the set of [[natural numbers]]:
*It is infinite.
*It has the [[Archimedean property]], in that there are no infinitesimals nor is there a largest element.
*It is [[well-ordered]] (in other words, it is [[well-founded]] and [[linearly ordered]]). That is, every subset of the natural numbers has a smallest element.
Thus, if we deem any given natural number ''the smallest'' "very, very large" number (which we can do by above), [[Almost all|all but finitely many]] natural numbers are "very, very large".
==See also==
*[[Natural numbers]]
*[[Asymptotic analysis]]
*[[Sufficiently large]]
[[Category:Mathematical terminology]]
[[Category:Mathematical notation]]
==References==
*{{mathworld|urlname=FrivolousTheoremofArithmetic|title=Frivolous Theorem of Arithmetic}}
