√100以上 tree(3) vs graham's number 428715-Tree(3) vs graham's number

Graham's Number used to be the biggest number I could name, but now I understand that TREE (3) ( https//enwikipediaorg/wiki/Kruskal%27s_tree_theorem ) is bigger still by a truly incredible amount (and TREE (1) = 1, and TREE (2) = 3) Unfortunately I don't understand that Wiki pageReply mrsmspin on March 26, 17 at 1031 pmThe Graham number is a figure that measures a stock's fundamental value by taking into account the company's earnings per share and book value per share The Graham number is the upper bound of

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Tree(3) vs graham's number

Tree(3) vs graham's number-TREE(3) is indistinguishable from zero compared to Loader's number1, which basically takes every bit pattern up to some n and expresses this as a program in the Calculus of Constructions This system is a bit weaker than being Turing complete, but the programs do always terminate (this makes the number computable compared with, say, the Busy Beaver number which does a similar thing with Turing complete programs)Later on, Graham showed that the upper bound to for this riddle is much much smaller than Graham's number, but still huge TREE(3) Equations aren't just useful' they're often beautiful

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Graham's Number – literally big enough to collapse your head into a black hole Graham's Number is a number so big that it would literally collapse your head into a black hole were you fully able to comprehend it And that's not hyperbole – the informational content of Graham's Number is so astronomically large that it exceeds the maximum amount of entropy that could be stored in aIt seems the Arildno number is a dwarf, after allTREE(3) is indistinguishable from zero compared to Loader's number1, which basically takes every bit pattern up to some n and expresses this as a program in the Calculus of Constructions This system is a bit weaker than being Turing complete, but the programs do always terminate (this makes the number computable compared with, say, the Busy Beaver number which does a similar thing with Turing complete programs)

These rules guarantee that the resulting longest tree sequence is finite When the input is 1 or 2, the length of the longest possible tree is small When it is 3, the length is VERY VERY VERY long TREE(3) dwarfs big numbers like Graham's number Big numbers like Graham's number are impossibly big, bigger than our universeGraham's number is an immense number that arose as an upper bound on the answer of a problem in the mathematical field of Ramsey theoryIt is named after mathematician Ronald Graham, who used the number in conversations with popular science writer Martin Gardner as a simplified explanation of the upper bounds of the problem he was working on In 1977, Gardner described the number in ScientificIf you replaced all the 3 's in the construction of Graham's number with TREE (3), the resulting number would be smaller than g T R E E (3) where g n denotes the n th number in Graham's sequence with g 64 being Graham's number This is much much smaller than TREE (4), for example

Given that, apparently TREE (1)=1 and TREE (2)=3, it seems quite surprising that TREE (3) should suddenly be far greater than Graham's Number, but there it is Just so you know, one way of expressing it is TREE (3)> {3,6,3 1 1¬1,222} That's enough of that, eh?TREE (3) is way beyond the scope of Grahams Number You couldnt even begin to express TREE (3) in any way besides the Fast Growing hierarchy Grahams number is only between f omega1 (63) and f omega1 (64) TREE (3) is beyond the gamma 0 of the hierarchy, which is way bigger than the omegasSo the first step of the Graham's function, 3↑↑↑↑3 = g 1, is very roughly A(6,6) The second step g 2 is roughly A(g 1,g 1) and the actual Graham's number, g 64, is roughly A(g 63,g 63) That's how big Graham's number is You can also use the iterated function notation with the Ackermann function to approximate Graham's number more

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Graham's Number Graham's number is connected to the following problem in the branch of mathematics known as Ramsey Theory Consider an ndimensional hypercube, and connect each pair of vertices to obtain a complete graph on 2 n vertices Then colour each of the edges of this graph either red or blueSo the first step of the Graham's function, 3↑↑↑↑3 = g 1, is very roughly A(6,6) The second step g 2 is roughly A(g 1,g 1) and the actual Graham's number, g 64, is roughly A(g 63,g 63) That's how big Graham's number is You can also use the iterated function notation with the Ackermann function to approximate Graham's number moreIn fact, $TREE(3)$ is a complete other league !

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Hello there This is Numberphile We mainly post videos about mathematics and just numbers in generalBut there's a huge difference between this problem and Graham's problem unlike the solution to Graham's problem, TREE(3) is not an upperbound It is known to be indeed be extremely huge, meaningActually, Graham's number is now considered pretty small by mathematicians For example, TREE(3) is so big that it makes Graham's number look like pretty much like zero in comparison The interesting thing about the TREE function is that it grows so rapidly eg TREE(1) = 1 TREE(2) = 3 TREE(3) = something insanely big!

Wrap Your Head Around The Enormity Of The Number Tree 3

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Other specific integers (such as TREE(3)) known to be far larger than Graham's number have since appeared in many serious mathematical proofs, for example in connection with Harvey Friedman's various finite forms of Kruskal's theorem Additionally, smaller upper bounds on the Ramsey theory problem from which Graham's number derived have since been proven to be validWhile TREE (n) is at f θ ( Ω ω) ( n)!Using parentheses to emphasize the top down order 3 3 3 3 = 3 3 (3 3) = 3 3 27 =3 (3 27) = 3 7,625,597,484,987 = a 36 trilliondigit number Remember, a googol and its universefilling microscopic minisand is only a 100digit number

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My big numbers videos https//wwwyoutubecom/playlist?list=PLDewy_4QBpjtYjxNVVRNrSaAIBSAOkBH6 Which is bigger?Graham's Number Let be the smallest dimension of a hypercube such that if the lines joining all pairs of corners are twocolored for any , a complete graph of one color with coplanar vertices will be forced Stated colloquially, this definition is equivalent to considering every possible committee from some number of people and enumerating every pair of committeesGrahams Number, the largest number used in a mathematical proof (so large you cant even comprehend how $&%ing big it is), is a factor of 3 (Ie g1= 3^^^^3 using the ^ for the Knuth uparrow notation and grahams number = g64 where each step from g1 to 64 the number of arrows is iterated from the previous number, so g1 is incomprehensible and g2 has g1 number of ^'s and so on)

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