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| − | The '''tragol''' is equal to {10,10,10,100,7} (10 hepohectodecated to 10) in [[BEAF]].<ref>{{cite web|first=Jonathan|last=Bowers|authorlink=Jonathan Bowers|url=http://www.polytope.net/hedrondude/scrapers.htm|title=Infinity Scrapers|accessdate=January 2013}}</ref> The term was coined by [[Chris Bird]]. |
+ | The '''tragol''' is equal to \(\{10,10,10,100,7\}\) (10 hepohectodecated to 10) in [[BEAF]].<ref>{{cite web|first=Jonathan|last=Bowers|authorlink=Jonathan Bowers|url=http://www.polytope.net/hedrondude/scrapers.htm|title=Infinity Scrapers|accessdate=January 2013}}</ref> The term was coined by [[Chris Bird]]. |
=== Etymology === |
=== Etymology === |
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| − | The name of the number is based on prefix "'''tri-'''" the number "[[gagol]]". |
+ | The name of the number is based on Latin prefix "'''tri-'''" and the number "[[gagol]]". |
| + | |||
=== Approximations === |
=== Approximations === |
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{| border="0" cellpadding="1" cellspacing="1" class="article-table" style="width: 500px;" |
{| border="0" cellpadding="1" cellspacing="1" class="article-table" style="width: 500px;" |
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! scope="col"|Notation |
! scope="col"|Notation |
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! scope="col"|Approximation |
! scope="col"|Approximation |
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| + | |- |
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| + | |[[Bird's array notation]] |
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| + | |\(\{10,10,10,100,7\}\) (exactly equal) |
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|- |
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|[[Hyper-E notation]] |
|[[Hyper-E notation]] |
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| − | |\(E100\# |
+ | |\(\textrm E100\#\#\#\#8\) |
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|- |
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|[[Chained arrow notation#Peter Hurford's extensions|Chained arrow notation]] |
|[[Chained arrow notation#Peter Hurford's extensions|Chained arrow notation]] |
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|\(H_{\omega^{(\omega^2) 7}}(100)\) |
|\(H_{\omega^{(\omega^2) 7}}(100)\) |
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|- |
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| + | |[[Slow-growing hierarchy]] (with [[List of systems of fundamental sequences#Fundamental_sequences_for_limit_ordinals_of_finitary_Veblen_function|this]] system of fundamental sequences) |
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| − | |[[Slow-growing hierarchy]] |
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|\(g_{\varphi(6,\omega,\omega,0)}(100)\) |
|\(g_{\varphi(6,\omega,\omega,0)}(100)\) |
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| − | === Number Navigator === |
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| − | {{numnav|troggolplex|tragolplex}} |
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=== Sources === |
=== Sources === |
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[[Category:Numbers]] |
[[Category:Numbers]] |
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[[Category:Numbers by Jonathan Bowers]] |
[[Category:Numbers by Jonathan Bowers]] |
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| − | [[Category:5-6 entry linear array notation level]] |
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[[Category:5+ linear]] |
[[Category:5+ linear]] |
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| + | [[Category:Googol series]] |
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| + | [[Category:BEAF]] |
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| + | [[Category:Quadratic omega level]] |
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| + | [[Category:Troogol series]] |
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Revision as of 02:18, 31 December 2020
The tragol is equal to \(\{10,10,10,100,7\}\) (10 hepohectodecated to 10) in BEAF.[1] The term was coined by Chris Bird.
Etymology
The name of the number is based on Latin prefix "tri-" and the number "gagol".
Approximations
| Notation | Approximation |
|---|---|
| Bird's array notation | \(\{10,10,10,100,7\}\) (exactly equal) |
| Hyper-E notation | \(\textrm E100\#\#\#\#8\) |
| Chained arrow notation | \(100 \rightarrow_8 100\) |
| Fast-growing hierarchy | \(f_{(\omega^2) 7}(100)\) |
| Hardy hierarchy | \(H_{\omega^{(\omega^2) 7}}(100)\) |
| Slow-growing hierarchy (with this system of fundamental sequences) | \(g_{\varphi(6,\omega,\omega,0)}(100)\) |
Sources
- ↑ Bowers, Jonathan. Infinity Scrapers. Retrieved January 2013.
See also
Googol series: googol(plex/duplex/triplex/quadraplex/quinplex) · giggol(plex/duplex) · gaggol(plex/duplex) · geegol(plex) · gigol(plex) · goggol(plex) · gagol(plex)
Boogol series: boogol(plex/duplex/triplex) · biggol(plex/duplex) · baggol(plex) · beegol(plex) · bigol · boggol · bagol
Troogol series: troogol(plex/duplex) · triggol(plex/duplex) · traggol(plex/duplex) · treegol · trigol · troggol · tragol
Quadroogol series: quadroogol(plex/duplex) · quadriggol(plex) · quadraggol · quadreegol · quadrigol · quadroggol · quadragol
Quintoogol series: quintoogol(plex) · quintiggol · quintaggol · quinteegol · quintigol · quintagol
Sextoogol series: sextoogol · septoogol · octoogol
Goobol series: goobol(plex) · gibbol · gabbol · geebol · gibol · gobbol · gabol
Boobol series: boobol · bibbol · babbol · beebol · bibol · bobbol · babol
Troobol series: troobol · tribbol · trabbol
Quadroobol series: quadroobol · quadribbol · quadrabbol · (quintoobol)
Gootrol series: gootrol · gitrol · gatrol · geetrol · gietrol · gotrol · gaitrol
Bootrol series: bootrol · trootrol · quadrootrol
Gooquadrol series: gooquadrol · booquadrol · quadreequadrol · (gooquintol)
Gossol series: gossol(plex) · gissol · gassol · geesol(plex) · gussol
Mossol series: mossol(plex) · missol · massol · meesol · mussol
Bossol series: bossol · bissol · bassol · beesol · bussol
Trossol series: trossol · trissol · trassol · treesol · trussol · (quadrossol · quintossol)
Dubol series: dubol · dutrol · duquadrol · dossol(plex)