There are clearly many interesting whole numbers. For instance, 2 is the only even prime number, 3 is the first odd prime, 6 is a perfect number (the sum of the proper divisors is the number itself), etc.<\/p>\n\n\n\n
But did you know that all whole numbers are interesting? We shall prove it here.<\/p>\n\n\n\n
Suppose, for the sake of contradiction, that not all whole numbers are interesting. Using the\u00a0well-ordering\u00a0property of the whole numbers, among the non-interesting numbers there is a smallest non-interesting number N. But that would make N interesting, after all, a contradiction.<\/p>\n\n\n\n
Therefore all numbers are interesting.<\/p>\n\n\n\n
The\u00a0Math\u00a0Behind\u00a0the\u00a0Fact:<\/strong> How to Cite this Page:<\/strong> Fun Fact suggested by:<\/strong> There are clearly many interesting whole numbers. For instance, 2 is the only even prime number, 3 is the first...<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[4,12,18,49,51],"class_list":["post-427","page","type-page","status-publish","hentry","tag-medium","tag-other","tag-paradox","tag-prime","tag-proof-by-contradiction"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/427","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/comments?post=427"}],"version-history":[{"count":4,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/427\/revisions"}],"predecessor-version":[{"id":1267,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/427\/revisions\/1267"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/media?parent=427"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/tags?post=427"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
This is a rather amusing model of a proof by\u00a0contradiction, and perhaps shouldn’t be taken too seriously!<\/p>\n\n\n\n
Su, Francis E., et al. “All Numbers are Interesting.” Math Fun Facts<\/em>. <http:\/\/www.math.hmc.edu\/funfacts>.<\/p>\n\n\n\n
Francis Su<\/p>\n","protected":false},"excerpt":{"rendered":"