Is Rayo's Number the Largest Finite Number?

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SUMMARY

The discussion centers around Rayo's Number, which is proposed as the largest finite number, contrasting it with Graham's Number, historically recognized as the largest number used in a mathematical paper. Participants highlight the conceptual challenges of defining and comparing such large numbers, emphasizing that Graham's Number is so vast it cannot be expressed within the observable universe. The conversation also touches on the philosophical implications of infinity and the triviality of simply inventing larger numbers without mathematical rigor.

PREREQUISITES
  • Understanding of large numbers, specifically Graham's Number.
  • Familiarity with mathematical concepts of infinity.
  • Basic knowledge of number theory and mathematical notation.
  • Awareness of the historical context of mathematical discussions, including notable figures like Ronald Graham.
NEXT STEPS
  • Research the properties and implications of Graham's Number in mathematical literature.
  • Explore the concept of Rayo's Number and its definition in mathematical terms.
  • Study the philosophical discussions surrounding infinity and its implications in mathematics.
  • Watch the Numberphile video on Tree3 to understand advanced concepts related to large numbers.
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Mathematicians, students of mathematics, and enthusiasts interested in the concepts of large numbers and their philosophical implications.

donglepuss
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i'll start:

1/(1-0.999...)
 
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Norton Juster and Jules Feiffer suggest this:

1661550568242.png

fresh_42 said:
I'll skip to the end: Ben Gurion!
http://www.ephraimkishon.de/en/my_favorite_stories.htm
 
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donglepuss said:
i'll start:

1/(1-0.999...)
1/(1-0.999...) +1

The problem is that it is s trivial game if all you have to do is make up a number.

That's why I'm a fan of Grahams Number, which was (for a time) the largest number ever used in a math paper.

Its so large that it cannot be written out in the volume of the observable universe. In fact, the number that represents the number of digits in Grahams number is so large, it cannot be written out in the volume of the known universe.
 
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donglepuss said:
i'll start:

1/(1-0.999...)
Bogus, since 9-bar is exactly 1 so you are dividing by zero. Why not just say infinity, since that's what you wrote?

EDIT: also, infinity is not a number, so you have violated your own rules of the question.
 
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I'm sure Dr. Seuss could tell you. (I don't recall the name of the book, sorry!)

-Dan
 
14

1661551864954.png
 
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donglepuss said:
i'll start:

1/(1-0.999...)
Two philosophers getting drunk in a bar and one asks the other.
"i bet you half a crown that I can think of a bigger number than you."
The other guy thought for a minute and said.
"Ok you're on."
First philosopher thought hard for about 5 minutes in silence then blurted out in triumph.
"Two!"
The second guy thought for a while and said.
"Ok you win."
 
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DaveC426913 said:
1/(1-0.999...) +1

The problem is that it is s trivial game if all you have to do is make up a number.

That's why I'm a fan of Grahams Number, which was (for a time) the largest number ever used in a math paper.

Its so large that it cannot be written out in the volume of the observable universe. In fact, the number that represents the number of digits in Grahams number is so large, it cannot be written out in the volume of the known universe.
Here is the man himself explaining where it came from.
Tree3 on numberphile is also interesting

EDIT: It would help if I posted the link. He died July 2020, I missed that. RIP Ronald Graham.
 
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  • #10
<inhales lung full of helium> ##{}^\mathrm{Two!}##

There, bet that's higher than any of you can manage.
 
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  • #11
donglepuss said:
i'll start:

1/(1-0.999...)
Is this the biggest? Rayo's number?

 

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