查看“︁拉約數”︁的源代码

'''拉約數'''（英語：Rayo's number），是一個由阿古斯丁·拉約（Agustín Rayo）所創造並命名的[[大數 (數學)|大數]]<ref name="CH. Rayo's Number">{{cite web | title = CH. Rayo's Number | url = http://mathfactor.uark.edu/2007/04/ch-rayos-number/ | publisher = The Math Factor Podcast | accessdate = 2014-03-24 | archive-date = 2014-03-24 | archive-url = https://web.archive.org/web/20140324172127/http://mathfactor.uark.edu/2007/04/ch-rayos-number/ | dead-url = no }}</ref><ref>{{cite web | last = Kerr | first = Josh | title = Name the biggest number contest | url = http://joshkerr.com/who-can-name-the-bigger-number-contest/ | accessdate = 2014-03-27 | date = 2013-12-07 | archiveurl = https://web.archive.org/web/20160320033110/http://www.joshkerr.com/who-can-name-the-bigger-number-contest/ | archivedate = 2016-03-20}}</ref>。這個數在當時比其他任何數都來得大（後來出現一個叫做BIG FOOT的大數比它更大<ref>{{cite web | title= Googology Wiki | url= http://googology.wikia.com/wiki/BIG_FOOT | accessdate= 2015-03-14 | archive-date= 2018-08-31 | archive-url= https://web.archive.org/web/20180831215510/http://googology.wikia.com/wiki/BIG_FOOT | dead-url= no }}</ref><ref>{{cite web|last=Wojowu and Nathan Ho|url=http://snappizz.com/foot|title=First-order oodle theory|work=snappizz.com|accessdate=2014-11-11|deadurl=yes|archiveurl=https://web.archive.org/web/20141105005518/http://snappizz.com/foot|archivedate=2014-11-05}}</ref><ref>{{cite web |url=http://googology.wikia.com/wiki/User_blog:LittlePeng9/FOOT_is_not_as_strong_as_I_thought |title=FOOT is not as strong as I thought |website=LittlePeng9's user blog |access-date=2017-04-20 |archive-date=2017-05-18 |archive-url=https://web.archive.org/web/20170518081728/http://googology.wikia.com/wiki/User_blog:LittlePeng9/FOOT_is_not_as_strong_as_I_thought |dead-url=no }}</ref>），就算是[[葛立恆數]]，跟拉約數比起來也是微不足道的。<ref>{{cite web|title=CH. Rayo's Number|url=http://mathfactor.uark.edu/2007/04/ch-rayos-number/|publisher=The Math Factor Podcast|accessdate=2014-05-24|archive-date=2014-03-24|archive-url=https://web.archive.org/web/20140324172127/http://mathfactor.uark.edu/2007/04/ch-rayos-number/|dead-url=no}}</ref><ref>{{cite web|last=Kerr|first=Josh|title=Name the biggest number contest|url=http://joshkerr.com/who-can-name-the-bigger-number-contest/|accessdate=2014-03-27|date=2013-12-07|deadurl=yes|archiveurl=https://web.archive.org/web/20160320033110/http://www.joshkerr.com/who-can-name-the-bigger-number-contest/|archivedate=2016-03-20}}</ref>這個數是在[[麻省理工學院]]在2007年1月26日舉辦的一場「大數戰鬥」中被定義的。<ref>{{cite web|last=Elga|first=Adam|title=Large Number Championship|url=//web.mit.edu/philos/www/poster.pdf|accessdate=2014-03-24|archive-date=2014-01-23|archive-url=https://web.archive.org/web/20140123055621/http://web.mit.edu/philos/www/poster.pdf|dead-url=no}}</ref><ref name="tech">{{cite news|last=Manzari|first=Mandana|title=Profs Duke It Out in Big Number Duel|url=http://tech.mit.edu/V126/N64/64largenumber.html|accessdate=2014-05-24|newspaper=The Tech|date=2007-01-31|author2=Nick Semenkovich|archive-date=2014-07-16|archive-url=https://web.archive.org/web/20140716012911/http://tech.mit.edu/V126/N64/64largenumber.html|dead-url=no}}</ref>

== 定義 ==
拉約數最初被定義為：<ref name="rayo">{{cite web|last=Rayo|first=Augustin|title=Big Number Duel|url=http://web.mit.edu/arayo/www/bignums.html|accessdate=2014-03-24|archive-date=2014-02-27|archive-url=https://web.archive.org/web/20140227043429/http://web.mit.edu/arayo/www/bignums.html|dead-url=no}}</ref>

:符合「大於任何使用[[集合論]]語言，並用不超過[[古戈爾]]個符號所能表示的數」的最小數

後來它被重新定義為「符合『大於任何使用[[一階邏輯]]語言，並用不超過[[古戈爾]]個符號所能表示的數』的最小數」。<ref name="tech" />

這個數的正式定義使用了[[二階邏輯]]，在下式中，<math>[\phi]</math>為[[哥德爾數|哥德爾編號]]，而<math>s</math>則代表一個可被賦值的變數：<ref name="rayo" />

 ∀R {
 {for any (coded) formula [ψ] and any variable assignment t
 (R([ψ], t) ↔
 (([ψ] = `x_i ∈ x_j' ∧ t(x_1) ∈ t(x_j)) ∨
 ([ψ] = `x_i = x_j' ∧ t(x_1) = t(x_j)) ∨
 ([ψ] = `(∼θ)' ∧ ∼R([θ], t)) ∨
 ([ψ] = `(θ∧ξ)' ∧ R([θ], t) ∧ R([ξ], t)) ∨
 ([ψ] = `∃x_i (θ)' and, for some an xi-variant t' of t, R([θ], t'))
 )} →
 R([φ], s)}

== 參考文獻 ==
{{Reflist}}

{{大數}}

[[Category:大整数]]