... [ ]
I thought if you multiply two integers together, you get an integer. But apparently you don't in PHP. You get a floating point number, which gets bigger and bigger and that's okay. Until you get to factorial(171), and then you get "
INF ". I don't know what "INF" is. I think it's infinity actually. But in that case, it's probably wrong, because infinity is awfully big. Bigger than factorial(171).
—Joe Armstrong
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{\displaystyle (|1)=\psi (\Omega )}
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{\displaystyle (1|1)=\psi (\Omega )+1}
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{\displaystyle (2|1)=\psi (\Omega )+2}
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{\displaystyle (3|1)=\psi (\Omega )+\omega }
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{\displaystyle ((3|0)|1)=\psi (\Omega )+\omega ^{\omega }}
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{\displaystyle (((3|0)|0)|1)=\psi (\Omega )+\omega ^{\omega ^{\omega }}}
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{\displaystyle ((((3|0)|0)|0)|1)=\psi (\Omega )+\omega ^{\omega ^{\omega ^{\omega }}}}
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{\displaystyle ((|1)|1)=\psi (\Omega )+\psi (\Omega )}
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{\displaystyle ((|1),(|1)|1)=\psi (\Omega )+\psi (\Omega )+\psi (\Omega )}
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{\displaystyle ((|1),(|1)|1)=\psi (\Omega )\omega }
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{\displaystyle ((|1),,(|1)|1)=\psi (\Omega )\omega ^{2}}
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{\displaystyle ((|1),,,(|1)|1)=\psi (\Omega )\omega ^{3}}
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{\displaystyle ((|1),,,,(|1)|1)=\psi (\Omega )\omega ^{4}}
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{\displaystyle ((|1)[(3|0)](|1)|1)=\psi (\Omega )\omega ^{\omega }}
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{\displaystyle ((|1)[([(3|0)]|0)](|1)|1)=\psi (\Omega )\omega ^{\omega ^{\omega }}}
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{\displaystyle ((|1)[([([(3|0)]|0)]|0)](|1)|1)=\psi (\Omega )\omega ^{\omega ^{\omega ^{\omega }}}}
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{\displaystyle ((|1)[(|1)](|1)|1)=\psi (\Omega )^{2}}
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{\displaystyle ((|1)[(|1)](|1)|1)=\psi (\Omega )\psi (\Omega )}
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{\displaystyle ((|1)[(|1)](|1)!!,!!(|1)[(|1)](|1)|1)=\psi (\Omega )\psi (\Omega )2}
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{\displaystyle ((|1)[(|1)](|1)!!,,!!(|1)[(|1)](|1)|1)=\psi (\Omega )\psi (\Omega )\omega ^{2}}
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{\displaystyle ((|1)[(|1)](|1)!!,,,!!(|1)[(|1)](|1)|1)=\psi (\Omega )\psi (\Omega )\omega ^{\omega }}
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{\displaystyle ((|1)[(|1)](|1)!![(1|0)]!!(|1)[(|1)](|1)|1)=\psi (\Omega )\psi (\Omega )\omega ^{\omega ^{\omega }}}
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{\displaystyle ((|1)[(|1)](|1)!![([(1|0)]|0)]!!(|1)[(|1)](|1)|1)=\psi (\Omega )\psi (\Omega )\omega ^{\omega ^{\omega ^{\omega }}}}
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{\displaystyle ((|1)[(|1)](|1)!![(|1)]!!(|1)[(|1)](|1)|1)=\psi (\Omega )\psi (\Omega )\psi (\Omega )}
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{\displaystyle ((|1)[(|1)](|1)!![(|1)]!!(|1)[(|1)](|1)|1)=\psi (\Omega )^{3}}
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{\displaystyle ((|1)[(|1)](|1)!!...![(|1)]!^{(3|0)}..!!(|1)[(|1)](|1)|1)=\psi (\Omega )^{\omega }}
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{\displaystyle ((|1)[(|1)](|1)!!...![(|1)]!^{(3,1|0)}..!!(|1)[(|1)](|1)|1)=\psi (\Omega )^{\omega +1}}
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{\displaystyle ((|1)[(|1)](|1)!!...![(|1)]!^{(3,2|0)}..!!(|1)[(|1)](|1)|1)=\psi (\Omega )^{\omega +2}}
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{\displaystyle ((|1)[(|1)](|1)!!...![(|1)]!^{(3,3|0)}..!!(|1)[(|1)](|1)|1)=\psi (\Omega )^{\omega 2}}
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{\displaystyle ((|1)[(|1)](|1)!!...![(|1)]!^{(3,,3|0)}..!!(|1)[(|1)](|1)|1)=\psi (\Omega )^{\omega ^{2}}}
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{\displaystyle ((|1)[(|1)](|1)!!...![(|1)]!^{(3,,,3|0)}..!!(|1)[(|1)](|1)|1)=\psi (\Omega )^{\omega ^{3}}}
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{\displaystyle ((|1)[(|1)](|1)!!...![(|1)]!^{(3,,,3|0)}..!!(|1)[(|1)](|1)|1)=\psi (\Omega )^{\omega ^{\omega }}}
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{\displaystyle ((|1)[(|1)](|1)!!...![(|1)]!^{(3((3,,,3|0))3|0)}..!!(|1)[(|1)](|1)|1)=\psi (\Omega )^{\omega ^{\omega ^{\omega }}}}
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{\displaystyle ((|1)[(|1)](|1)!!...![(|1)]!^{[(|1)]}..!!(|1)[(|1)](|1)|1)=\psi (\Omega )^{\psi (\Omega )}}
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{\displaystyle ((|1)[(|1)](|1)!!...![(|1)]!^{((|1)[(|1)](|1)!!...![(|1)]!^{[(|1)]}..!!(|1)[(|1)](|1)|1)}..!!(|1)[(|1)](|1)|1)=\psi (\Omega )^{\psi (\Omega )^{\psi (\Omega )}}}
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{\displaystyle ((|1)[(|1)](|1)!!...![(|1)]!^{((|1)[(|1)](|1)!!...![(|1)]!^{[(|1)]}..!!(|1)[(|1)](|1)|1)}..!!(|1)[(|1)](|1)|1)=\psi (\Omega )^{\psi (\Omega )^{\psi (\Omega )}}}
...
|1)=\psi (\Omega )\omega ^{\omega }}](https://services.fandom.com/mathoid-facade/v1/media/math/render/svg/26c9c70980cc0a366b32dc5d0266e0bfb402eb56)
![{\displaystyle ((|1)[([(3|0)]|0)](|1)|1)=\psi (\Omega )\omega ^{\omega ^{\omega }}}](https://services.fandom.com/mathoid-facade/v1/media/math/render/svg/673f168c89d50a92ccf402e6a6e13fa4d69e4577)
![{\displaystyle ((|1)[([([(3|0)]|0)]|0)](|1)|1)=\psi (\Omega )\omega ^{\omega ^{\omega ^{\omega }}}}](https://services.fandom.com/mathoid-facade/v1/media/math/render/svg/42ba01fc6fbf71c7c29d444c944018269d256fbb)
|1)=\psi (\Omega )^{2}}](https://services.fandom.com/mathoid-facade/v1/media/math/render/svg/8a841535657c4c3f6ef8a3ddb871f9b9df971e9c)
|1)=\psi (\Omega )\psi (\Omega )}](https://services.fandom.com/mathoid-facade/v1/media/math/render/svg/054cf99eef230b30d0e2bb3cbd0a68062950b881)
!!,!!(|1)[(|1)](|1)|1)=\psi (\Omega )\psi (\Omega )2}](https://services.fandom.com/mathoid-facade/v1/media/math/render/svg/5d69b9286c513beebfe92161c92f2103a2049525)
!!,,!!(|1)[(|1)](|1)|1)=\psi (\Omega )\psi (\Omega )\omega ^{2}}](https://services.fandom.com/mathoid-facade/v1/media/math/render/svg/1f656165195027f407b22a9f764012e1eea2e5d4)
!!,,,!!(|1)[(|1)](|1)|1)=\psi (\Omega )\psi (\Omega )\omega ^{\omega }}](https://services.fandom.com/mathoid-facade/v1/media/math/render/svg/39869c726842ed1a6e72fc8e88947218e827d289)
!![(1|0)]!!(|1)[(|1)](|1)|1)=\psi (\Omega )\psi (\Omega )\omega ^{\omega ^{\omega }}}](https://services.fandom.com/mathoid-facade/v1/media/math/render/svg/ef2f474c0d8c13b721fc8b2f41831f36a64c3142)
!![([(1|0)]|0)]!!(|1)[(|1)](|1)|1)=\psi (\Omega )\psi (\Omega )\omega ^{\omega ^{\omega ^{\omega }}}}](https://services.fandom.com/mathoid-facade/v1/media/math/render/svg/80ce803025e2e3bb963d79d5e21ef24d7663433e)
!![(|1)]!!(|1)[(|1)](|1)|1)=\psi (\Omega )\psi (\Omega )\psi (\Omega )}](https://services.fandom.com/mathoid-facade/v1/media/math/render/svg/b0cab62a0a711e7035006f9ea3a9360a0da07ce6)
!![(|1)]!!(|1)[(|1)](|1)|1)=\psi (\Omega )^{3}}](https://services.fandom.com/mathoid-facade/v1/media/math/render/svg/b3a13121b3c9c7a65faed46985bb706831e85e82)
!!...![(|1)]!^{(3|0)}..!!(|1)[(|1)](|1)|1)=\psi (\Omega )^{\omega }}](https://services.fandom.com/mathoid-facade/v1/media/math/render/svg/681954a90716de920d072fe8364389556f6bf357)
!!...![(|1)]!^{(3,1|0)}..!!(|1)[(|1)](|1)|1)=\psi (\Omega )^{\omega +1}}](https://services.fandom.com/mathoid-facade/v1/media/math/render/svg/6f0ef5443fa425599f09134b69b7b693fcaeb55c)
!!...![(|1)]!^{(3,2|0)}..!!(|1)[(|1)](|1)|1)=\psi (\Omega )^{\omega +2}}](https://services.fandom.com/mathoid-facade/v1/media/math/render/svg/dea86d2c0253d94d6081b122da10fd6d397ef1de)
!!...![(|1)]!^{(3,3|0)}..!!(|1)[(|1)](|1)|1)=\psi (\Omega )^{\omega 2}}](https://services.fandom.com/mathoid-facade/v1/media/math/render/svg/3e09e382b214387e981c9ea11ee3f235b568f44f)
!!...![(|1)]!^{(3,,3|0)}..!!(|1)[(|1)](|1)|1)=\psi (\Omega )^{\omega ^{2}}}](https://services.fandom.com/mathoid-facade/v1/media/math/render/svg/57dc1a61c49f74608f31c35b6bdaf36fe2202720)
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