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Graham

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  • Richard DeemingR Richard Deeming

    Because all smaller numbers are irrelevant. ;P Graham's number[^] From 1,000,000 to Graham’s Number[^]


    "These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer

    M Offline
    M Offline
    Mark_Wallace
    wrote on last edited by
    #7

    That's crackers.

    I wanna be a eunuchs developer! Pass me a bread knife!

    1 Reply Last reply
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    • Richard DeemingR Richard Deeming

      Because all smaller numbers are irrelevant. ;P Graham's number[^] From 1,000,000 to Graham’s Number[^]


      "These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer

      D Offline
      D Offline
      Daniel Pfeffer
      wrote on last edited by
      #8

      The TREE sequence begins TREE(1) = 1, TREE(2) = 3, then suddenly TREE(3) explodes to a value so enormously large that many other "large" combinatorial constants, such as Friedman's n(4),[*] are extremely small by comparison.[1] A lower bound for n(4), and hence an extremely weak lower bound for TREE(3), is A(A(...A(1)...)), where the number of As is A(187196),[2] and A() is a version of Ackermann's function: A(x) = 2 [x + 1] x in hyperoperation. Graham's number, for example, is approximately A^64(4) which is much smaller than the lower bound A^A(187196)(1). http://en.wikipedia.org/wiki/Kruskal%27s_tree_theorem#Friedman.27s_finite_form[^] I think it's time that we all went home...

      If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill

      Richard DeemingR K 2 Replies Last reply
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      • Richard DeemingR Richard Deeming

        Indeed, and so much more interesting than ∞. :)


        "These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer

        D Offline
        D Offline
        Daniel Pfeffer
        wrote on last edited by
        #9

        All natural integers are interesting. (The proof is left as an exercise for the student)

        If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill

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        • D Daniel Pfeffer

          The TREE sequence begins TREE(1) = 1, TREE(2) = 3, then suddenly TREE(3) explodes to a value so enormously large that many other "large" combinatorial constants, such as Friedman's n(4),[*] are extremely small by comparison.[1] A lower bound for n(4), and hence an extremely weak lower bound for TREE(3), is A(A(...A(1)...)), where the number of As is A(187196),[2] and A() is a version of Ackermann's function: A(x) = 2 [x + 1] x in hyperoperation. Graham's number, for example, is approximately A^64(4) which is much smaller than the lower bound A^A(187196)(1). http://en.wikipedia.org/wiki/Kruskal%27s_tree_theorem#Friedman.27s_finite_form[^] I think it's time that we all went home...

          If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill

          Richard DeemingR Offline
          Richard DeemingR Offline
          Richard Deeming
          wrote on last edited by
          #10

          Daniel Pfeffer wrote:

          I think it's time that we all went home...

          Apart from those of us who work from home, who should all go down the pub. :rolleyes:


          "These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer

          "These people looked deep within my soul and assigned me a number based on the order in which I joined" - Homer

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          • Richard DeemingR Richard Deeming

            Daniel Pfeffer wrote:

            I think it's time that we all went home...

            Apart from those of us who work from home, who should all go down the pub. :rolleyes:


            "These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer

            D Offline
            D Offline
            Daniel Pfeffer
            wrote on last edited by
            #11

            :thumbsup::thumbsup::thumbsup:

            If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill

            1 Reply Last reply
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            • Richard DeemingR Richard Deeming

              Because all smaller numbers are irrelevant. ;P Graham's number[^] From 1,000,000 to Graham’s Number[^]


              "These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer

              C Offline
              C Offline
              Corporal Agarn
              wrote on last edited by
              #12

              So the U.S. debt is trying to surpass Graham's number?

              Mongo: Mongo only pawn... in game of life.

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              • Richard DeemingR Richard Deeming

                Because all smaller numbers are irrelevant. ;P Graham's number[^] From 1,000,000 to Graham’s Number[^]


                "These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer

                G Offline
                G Offline
                Gary Wheeler
                wrote on last edited by
                #13

                Any mathematicians in the crowd are watching the children play with matches.

                Software Zen: delete this;

                D 1 Reply Last reply
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                • D Daniel Pfeffer

                  The TREE sequence begins TREE(1) = 1, TREE(2) = 3, then suddenly TREE(3) explodes to a value so enormously large that many other "large" combinatorial constants, such as Friedman's n(4),[*] are extremely small by comparison.[1] A lower bound for n(4), and hence an extremely weak lower bound for TREE(3), is A(A(...A(1)...)), where the number of As is A(187196),[2] and A() is a version of Ackermann's function: A(x) = 2 [x + 1] x in hyperoperation. Graham's number, for example, is approximately A^64(4) which is much smaller than the lower bound A^A(187196)(1). http://en.wikipedia.org/wiki/Kruskal%27s_tree_theorem#Friedman.27s_finite_form[^] I think it's time that we all went home...

                  If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill

                  K Offline
                  K Offline
                  kmoorevs
                  wrote on last edited by
                  #14

                  Can you spell that sequence using only A, C, G, and T? :laugh:

                  "Go forth into the source" - Neal Morse

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                  • K kmoorevs

                    Can you spell that sequence using only A, C, G, and T? :laugh:

                    "Go forth into the source" - Neal Morse

                    D Offline
                    D Offline
                    Daniel Pfeffer
                    wrote on last edited by
                    #15

                    Yes, but the representation is too large to fit in the margins of Code Project :)

                    If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill

                    R 1 Reply Last reply
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                    • G Gary Wheeler

                      Any mathematicians in the crowd are watching the children play with matches.

                      Software Zen: delete this;

                      D Offline
                      D Offline
                      Daniel Pfeffer
                      wrote on last edited by
                      #16

                      Gary Wheeler wrote:

                      Any mathematicians in the crowd are watching the children play with matches.

                      For my next act, I will wrassle a bear, make peace with a feral Chtorran, and divide by zero! [Bonus points for identifying the references]

                      If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill

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                      • D Daniel Pfeffer

                        Gary Wheeler wrote:

                        Any mathematicians in the crowd are watching the children play with matches.

                        For my next act, I will wrassle a bear, make peace with a feral Chtorran, and divide by zero! [Bonus points for identifying the references]

                        If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill

                        E Offline
                        E Offline
                        eshill
                        wrote on last edited by
                        #17

                        "Then for my first encore, I drink a whole bottle of trans-Lunar brandy, make love to a feral Chtorran, and kill a Martian woman-I think. Or maybe it's the other way around." David Gerrold in The Voyage of the Star Wolf. :)

                        D 1 Reply Last reply
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                        • Richard DeemingR Richard Deeming

                          Because all smaller numbers are irrelevant. ;P Graham's number[^] From 1,000,000 to Graham’s Number[^]


                          "These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer

                          M Offline
                          M Offline
                          Matthew Dennis
                          wrote on last edited by
                          #18

                          I think this is how mathematicians and astrophysists play "Mine's bigger than yours" :laugh:

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                          • E eshill

                            "Then for my first encore, I drink a whole bottle of trans-Lunar brandy, make love to a feral Chtorran, and kill a Martian woman-I think. Or maybe it's the other way around." David Gerrold in The Voyage of the Star Wolf. :)

                            D Offline
                            D Offline
                            Daniel Pfeffer
                            wrote on last edited by
                            #19

                            Correct!

                            If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill

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                            • D Daniel Pfeffer

                              Yes, but the representation is too large to fit in the margins of Code Project :)

                              If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill

                              R Offline
                              R Offline
                              racketeer
                              wrote on last edited by
                              #20

                              :laugh:

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