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<p style="font-weight:normal;font-size:16px;">[[Thousalogue|L((3))]] = \(10^{1000^{1000^{...^{1000<nowiki>}}}</nowiki>} (... = 1,000)\)</p> |
<p style="font-weight:normal;font-size:16px;">[[Thousalogue|L((3))]] = \(10^{1000^{1000^{...^{1000<nowiki>}}}</nowiki>} (... = 1,000)\)</p> |
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| − | <p style="font-weight:normal;font-size:16px;">L((5))= 10^100,000^100,000^...^100,000 (... = 100,000)</p> |
+ | <p style="font-weight:normal;font-size:16px;">L((5))= \(10^{100,000^{100,000^{...^{100,000<nowiki>}}}</nowiki>} (... = 100,000)\)</p> |
| − | <p style="font-weight:normal;font-size:16px;">L((33))= 10^decillion^decillion^...^decillion (... = decillion)</p> |
+ | <p style="font-weight:normal;font-size:16px;">L((33))= \(10^{decillion^{decillion^{...^{decillion<nowiki>}}}</nowiki>} (... = decillion)\)</p> |
| − | <p style="font-weight:normal;font-size:16px;">L((100))= 10^googol^googol^googol^...^googol (... = googol)</p> |
+ | <p style="font-weight:normal;font-size:16px;">L((100))= \(10^{googol^{googol^{googol^{...^{googol<nowiki>}}}</nowiki>} (... = googol)\)</p> |
| − | <p style="font-weight:normal;font-size:16px;">L((googol))= 10^googolplex^googolplex^...^googolplex (... = googolplex)</p> |
+ | <p style="font-weight:normal;font-size:16px;">L((googol))= \(10^{googolplex^{googolplex^{...^{googolplex<nowiki>}}}</nowiki>} (... = googolplex)\)</p> |
<p style="font-weight:normal;font-size:16px;"> |
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<p style="font-weight:normal;font-size:16px;">L(((100)))= <span style="line-height:normal;word-spacing:normal;word-wrap:normal;white-space:nowrap;direction:ltr;max-width:none;max-height:none;min-width:0px;min-height:0px;"><span style="vertical-align:0px;display:inline-block;line-height:normal;width:10.003em;"><span style="vertical-align:0px;display:inline-block;line-height:normal;width:8.336em;height:0px;font-size:19.2px;"><span style="vertical-align:0px;line-height:normal;"><span style="vertical-align:0px;line-height:normal;"><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Main;">10</span><span style="padding-left:0.263em;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">↑<span style="vertical-align:0px;line-height:normal;">↑</span></span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Main;">.</span><span style="padding-left:0.159em;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">.</span><span style="padding-left:0.159em;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">.</span><span style="padding-left:0.159em;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">↑<span style="vertical-align:0px;line-height:normal;">↑</span></span><span style="padding-left:0.263em;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">(</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">g</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">o</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">o</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">g</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">o</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">l</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Main;">)</span></span></span></span></span></span> with googol up arrows</p> |
<p style="font-weight:normal;font-size:16px;">L(((100)))= <span style="line-height:normal;word-spacing:normal;word-wrap:normal;white-space:nowrap;direction:ltr;max-width:none;max-height:none;min-width:0px;min-height:0px;"><span style="vertical-align:0px;display:inline-block;line-height:normal;width:10.003em;"><span style="vertical-align:0px;display:inline-block;line-height:normal;width:8.336em;height:0px;font-size:19.2px;"><span style="vertical-align:0px;line-height:normal;"><span style="vertical-align:0px;line-height:normal;"><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Main;">10</span><span style="padding-left:0.263em;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">↑<span style="vertical-align:0px;line-height:normal;">↑</span></span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Main;">.</span><span style="padding-left:0.159em;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">.</span><span style="padding-left:0.159em;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">.</span><span style="padding-left:0.159em;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">↑<span style="vertical-align:0px;line-height:normal;">↑</span></span><span style="padding-left:0.263em;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">(</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">g</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">o</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">o</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">g</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">o</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">l</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Main;">)</span></span></span></span></span></span> with googol up arrows</p> |
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| − | <p style="font-weight:normal;font-size:16px;">L(((googol)))= <span style="line-height:normal;word-spacing:normal;word-wrap:normal;white-space:nowrap;direction:ltr;max-width:none;max-height:none;min-width:0px;min-height:0px;"><span style="vertical-align:0px;display:inline-block;line-height:normal;width:12.19em;"><span style="vertical-align:0px;display:inline-block;line-height:normal;width:10.159em;height:0px;font-size:19.2px;"><span style="vertical-align:0px;line-height:normal;"><span style="vertical-align:0px;line-height:normal;"><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Main;">10</span><span style="padding-left:0.263em;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">↑<span style="vertical-align:0px;line-height:normal;">↑</span></span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Main;">.</span><span style="padding-left:0.159em;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">.</span><span style="padding-left:0.159em;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">.</span><span style="padding-left:0.159em;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">↑<span style="vertical-align:0px;line-height:normal;">↑</span></span><span style="padding-left:0.263em;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">(</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">g</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">o</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">o</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">g</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">o</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">l</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">p</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">l</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">e</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">x</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Main;">)</span></span></span></span></span></span>with googolplex up arrows</p> |
+ | <p style="font-weight:normal;font-size:16px;">\(L(((googol)))\)= <span style="line-height:normal;word-spacing:normal;word-wrap:normal;white-space:nowrap;direction:ltr;max-width:none;max-height:none;min-width:0px;min-height:0px;"><span style="vertical-align:0px;display:inline-block;line-height:normal;width:12.19em;"><span style="vertical-align:0px;display:inline-block;line-height:normal;width:10.159em;height:0px;font-size:19.2px;"><span style="vertical-align:0px;line-height:normal;"><span style="vertical-align:0px;line-height:normal;"><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Main;">10</span><span style="padding-left:0.263em;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">↑<span style="vertical-align:0px;line-height:normal;">↑</span></span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Main;">.</span><span style="padding-left:0.159em;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">.</span><span style="padding-left:0.159em;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">.</span><span style="padding-left:0.159em;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">↑<span style="vertical-align:0px;line-height:normal;">↑</span></span><span style="padding-left:0.263em;vertical-align:0px;line-height:normal;font-family:MathJax_Main;">(</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">g</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">o</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">o</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">g</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">o</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">l</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">p</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">l</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">e</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Math-italic;">x</span><span style="vertical-align:0px;line-height:normal;font-family:MathJax_Main;">)</span></span></span></span></span></span>with googolplex up arrows</p> |
<p style="font-weight:normal;font-size:16px;"> |
<p style="font-weight:normal;font-size:16px;"> |
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Revision as of 16:55, 23 October 2016
Hyper-Log notation or Hyper-L notation is an extension of the Log function that itself is a fast growing function, but not fast enough. Hyper-L notation is as follows. The standard notation is L(n) to indicate it is a hyper-L function.
First Order
Representation: L(n)
Rule: \(L(n)\)= reverse \(log(n)\) or \(revlog(n)\)
Examples:
\(L(5)\) = 100,000
\(L(33)\)= decillion
\(L(100)\)= googol
\(L(googol)\)= googolplex
Second Order
Representation: \(L((n))\)
Rule: \(L((n))\)= \(10^{revlog(n)^{revlog(n)^{...^{revlog(n)}}}}; where ...=revlog(n)\)
Examples:
L((3)) = \(10^{1000^{1000^{...^{1000}}}} (... = 1,000)\)
L((5))= \(10^{100,000^{100,000^{...^{100,000}}}} (... = 100,000)\)
L((33))= \(10^{decillion^{decillion^{...^{decillion}}}} (... = decillion)\)
L((100))= \(10^{googol^{googol^{googol^{...^{googol}}}} (... = googol)\)
L((googol))= \(10^{googolplex^{googolplex^{...^{googolplex}}}} (... = googolplex)\)
Third Order
Representation: L(((n)))
Rule: 10↑↑...↑↑(N)with revlog(n) up arrows
Examples:
L(((5)))= 10↑↑...↑↑(100,000)with 100,000 up arrows
L(((33)))= 10↑↑...↑↑(decillion)with decillion up arrows
L(((100)))= 10↑↑...↑↑(googol) with googol up arrows
\(L(((googol)))\)= 10↑↑...↑↑(googolplex)with googolplex up arrows