An ambitious plan

Jai Ganesh · 2008-02-04 01:54:59

Beleive me, One day I want my number to displace the place of Graham's Number!.
In the Guiness Book of World Records!
This is possible, consider the following facts....1. There's nothing as the highest number used in a mathematical proof, I am sure you would ageree with me.
2. The Ramsay Theory and Graham's Number are enough confusing to the mathematicians as they are to the rest of the literate community.
3. There's no upper limit whatsoever in Mathematics, compared to the other sciences....there are no boundaries, no limits, mathematicians are free thinkers......
4. I shall prepare the draft and all the other modalities shall be completed by me...I just require support from other members.....
5. I look forward to support from mathsyperson, Ricky, John, luca, Jane among others. Please help me in my pursuit. We shall, at the end of the day, jointly do it.
6. The method is quite simple......... First, I genearte a number that is bigger than the biggest conceived ever. Then, I create a even bigger number by saying that the number I had in my mind is the smallest number apart from zero and one which is a perfect square, cube, fourth, fifth, and nth poewer where n is the number I said earliewr.
7. Then, I ask mathsy to give me a valid, elegant and infallible proof that every 2^20nth power gives unlimited number of a string of digits such that their higher powers always end in themselves.
8. mathsy already has it in his mind, only it should pass the strenous test of the rigors of the number theorist! WE AT MATHSISFUN HAVE DONE IT, RECJOICE!!!!
9. The ball is in your court!
10. We owe this to humanity to obliterate a undeserving, unclear, and undecipherable world record! God only can save the Mathematics community, else the team at MathsIsFun can!

Zach · 2008-02-04 07:43:44

My new number is Zach's number. It is equal to Graham's Number! +1

mathsyperson · 2008-02-04 07:48:17

Great! Now use it in an original mathematical proof.

Zach · 2008-02-04 11:00:05

Zach's Number > Graham's Number.

This proves that my number is bigger.

MathsIsFun · 2008-02-04 12:14:29

Sounds a cool idea, Ganesh!

John E. Franklin · 2008-02-04 12:17:10

Sounds like fun!
Post links to the record that
needs breaking!

Jai Ganesh · 2008-02-06 03:14:30

For those of whom are interested in knowing what record is intended to be broken,
search for Graham's Number, Moser's, Knuth's up-arrow notation, Conways, chained arrow notation.

And now....Introducing to the world....the most elegant Rod Pierce Number or simply Rod Number or R....

Lest begin with the first prime number..2, and the first abundant number 12.
2^12 is 4096.

4096->4096->4096->4096->4096 is ganesh Number or g.
Here, the -> is the chained arrow notation as in John Conway's.

The smallest number apart from zero and one which is a perfect square, cube, fourth, fifth,... and gth power is mathsy number.

Rod number is the number xth power of 2 whereby mathsy number is reached.

Rod number is such a beautiful number; assuming its number of digits are m and last digits are m. Any power of R would always end in R.

The last digit of R is 6, and the last 10 digits of R is 1787109376. R is greater than G or Graham's Number by more than a mile!

q.e.d.

Mission Accomplished.

Jai Ganesh · 2008-02-06 03:29:50

mathsy, Ricky, Jane, luca......please take over from where I left.........
Lets make an attempt........
A brave effort is much better than something not done.......
mathsy and Jane.....we have already discussed this subject.......
Ricky..... the final assualt lies with you......you got to tell us whether we are on the right track or not....
and at ever step, luca and Jane, ensure there is no fallacy....

MathsIsFun · 2008-02-06 09:15:49

Cute names

But aside from that, I support this as a chance for us to work together on a project.

LuisRodg · 2008-02-06 10:27:43

Is it ok to say I have no idea what you guys are saying?

I googled Graham's number and the Wiki page was so confusing I wasnt able to understand anything....

Ricky · 2008-02-06 11:22:30

ganesh, I believe you have a misunderstanding of the record that Graham's number holds. It is the largest number that is used to prove something. In order to beat Graham's number, you must not only construct a larger number, but you must then use that number to prove something of value in the mathematical community.

mathsyperson · 2008-02-06 11:31:23

What is Graham's number used to prove, anyway?

LuisRodg · 2008-02-06 11:43:08

Taken from Wiki:

"Graham's number is connected to the following problem in the branch of mathematics known as Ramsey theory:

Consider an n-dimensional hypercube, and connect each pair of vertices to obtain a complete graph on 2n vertices. Then colour each of the edges of this graph using only the colours red and black. What is the smallest value of n for which every possible such colouring must necessarily contain a single-coloured complete sub-graph with 4 vertices which lie in a plane?

Although the solution to this problem is not yet known, Graham's number is the smallest known upper bound for it."

http://en.wikipedia.org/wiki/Graham's_number

Last edited by LuisRodg (2008-02-06 11:43:35)

MathsIsFun · 2008-02-06 12:24:19

I think ganesh is looking at the property "Any power of R would always end in R" ... he has done research on that before.

Ricky · 2008-02-06 12:30:04

I see now. Perhaps you could provide a reason as to why this is, ganesh

Jai Ganesh · 2008-02-06 17:40:51

Ladies, Gentlemen,
take your time! We are in no hurry!
Graham's Number entered the Guiness in 1976, it is already 32 years old!
As ricky rightly pointed out, we ought to generate a number greater than G,
Graham's Number, and then use it in an elegant mathematical proof, an infallible one, and one which ought to pass the litmus test of the rigorous number theorist!

Rod or Rod Number ends is 6, the first perfect number in the universe.
Powers of Numbers ending in 0,1, 5, and 6 end in themselves.

We have jointly worked on this before, generating numbers n such that higher powers of n have last digits same as n. I guess we got up to 50 digits.

2^(4*5^n) gives n digits of a number such that any power of n ends in n.

The smallest number apart from zero and one which is a perfect square, cube, fourth...... and nth power are always of the kind 2^(4*5^n).

When n=4096->4096->4096->4096->4096,
we get an enormously larger number than Graham's.

Hence, R>>G.

q.e.d.

MathsIsFun · 2008-02-06 18:10:07

Hmmm... but is choosing "n=4096->4096->4096->4096->4096" a necessary part of the proof? Otherwise we could simply have a proof that "n+1 is an integer" and choose "n=G" to have a proof containing a number greater than G, if you see what I mean.

Identity · 2008-02-06 19:07:22

Good luck with this, it sounds exciting!

MathsIsFun · 2008-02-09 11:44:10

Could we explore the concept of "ends with" (RxR ends with R)?

Ie 6x6=36 satisfies "ends with" in decimal. What is the general rule we are dealing with?

LuisRodg · 2008-02-09 12:25:15

7x7 = 49 so it doesnt end in 7?

mathsyperson · 2008-02-09 12:25:38

Every number that satisfies "ends with" (excluding 0 and 1) has exactly one (non-zero) digit that can be tacked on the front to produce another number that satisfies "ends with".

eg. 6 works, and so does 76. No other ?6 does though.

MathsIsFun · 2008-02-09 15:12:10

Perhaps it "forks" somewhere, ie there may sometimes be 2 or more digits for some power of 10.

Ganesh has studied this, and so maybe he can give us what he knows.

Maybe start a new thread for the "ends with" subject?

John E. Franklin · 2008-02-10 14:20:20

This hypercube is obviously not a binary-valued hypercube, because
the checkerboard filling is always possible.
I'll read more. Fun!!

John E. Franklin · 2008-02-10 14:38:41

Oh, I'm sorry, it is not the locations that are colored red or black, it
is the connecting lines between adjacent locations.

John E. Franklin · 2008-02-11 12:36:56

Hi again, I might have a way to fill in
a hypercube of any dimension so that
you avoid the square edges all being the
same color, using only two colors.
It is so very simple that it makes me
wonder what I am missing? First start
with two points and connect them and
paint the line Red. Next make a copy
of this object and negate the Red color
to Black. Now connect the the two
objects with connecting lines of any
color you want, shouldn't matter.
Now repeat this procedure of
copying the final object and negating
its component edges, and put in the
connecting lines of any color, and
I'm pretty sure, there will never be
any square you can make with all
the same color!!!! I love it!!!
Hope I get the concept!!!

Math Is Fun Forum

#1 2008-02-04 01:54:59

An ambitious plan

#2 2008-02-04 07:43:44

Re: An ambitious plan

#3 2008-02-04 07:48:17

Re: An ambitious plan

#4 2008-02-04 11:00:05

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#5 2008-02-04 12:14:29

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#6 2008-02-04 12:17:10

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#7 2008-02-06 03:14:30

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#8 2008-02-06 03:29:50

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#9 2008-02-06 09:15:49

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