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moose1997
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| Joined: 04 Jul 2008 |
| Total Posts: 12502 |
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| 10 Nov 2014 04:40 PM |
look up TREE(3) and tell me
here's a hint
This maximal length is a function of k, dubbed TREE(k). The first two values are TREE(1) = 1 and TREE(2) = 3. The next value, TREE(3) is famously very large. It exceeds Graham's number and nn(5)(5). Chris Bird has shown that TREE(3)>{3,6,3[1[1¬1,2]2]2}, using his array notation.
graham's # is
3^^^^3=g1
3^^...(g1 # of arrows)...^^3 = g2 repeat until
3^^...(g63 # of arrows)...^^3 = g64 g64 = Graham's Number (g)
In the words of Archimedes, give me a long enough lever and a place to rest it.. or I shall kill 1 hostage every hour. |
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| 10 Nov 2014 04:40 PM |
| What exactly happened to the "simple" part? |
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| 10 Nov 2014 04:44 PM |
3^3 = 9 (simple)
3^^3 = 3^3^3 = 3^27 = 7.6trillion (okay...)
3^^^3 = 3^3^3^3 = 3^3^27 = 3^7.6trillion = insurmountable value
3^^^^3 = 3^3^3^3^3 = 3^3^3^27 = 3^3^7.6trillion = 3^insurmountablevalue
3^insurmountable (henceforth known as U) so 3^U = g1
that's just g1
now g64
then tree(3)
In the words of Archimedes, give me a long enough lever and a place to rest it.. or I shall kill 1 hostage every hour. |
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| 10 Nov 2014 04:46 PM |
i havent even learned this crap yet and i thought algebra was hard now i have to do more of it |
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| 10 Nov 2014 04:49 PM |
the upper limit in ultrafinitism is
(794,843,294,078,147,843,293.7+1/30)⋅e^π^e^π
while being insanely large this number is nowhere close to g64 and is a spec of dust in comparison to TREE(3)
In the words of Archimedes, give me a long enough lever and a place to rest it.. or I shall kill 1 hostage every hour. |
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| 10 Nov 2014 04:50 PM |
do I get the award for most experimental OT thread
In the words of Archimedes, give me a long enough lever and a place to rest it.. or I shall kill 1 hostage every hour. |
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