What is the largest real number one can write within 200 characters?

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In summary: Edit: I see someone has edited the post - note I wasn't sure if the Knuth's notation counts as standard, so I have not used all possible up arrows, leaving place for the "Knuth's notation" name. If if counts as standard, then obviously there should be 198 up arrows.Well keeping in line with the above post, just do this:x!, x is Graham's number.That would be taking Graham's number factorial 176 times.Well keeping in line with the above post, just do this:x!, x is Graham's number.That would be taking Graham's number factorial 176 times.
  • #71
222222222222222222222222222222222222222

divided by .00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012222222222222222232
 
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  • #72
OrangeDog said:
222222222222222222222222222222222222222

divided by .00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012222222222222222232

Not even close to Graham's number alone. If you can write it using exponents, then it's much smaller than Graham's number. Actually, unfathomably smaller than Graham's number.
 
  • #73
OrangeDog said:
222222222222222222222222222222222222222

divided by .00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012222222222222222232

Not only does it vastly go over the character limit, it is also vastly smaller than Graham's number. No matter how many exponents you put in, there's not enough space and time in the universe for the exponent tower to get anywhere near Graham.
 
  • #74
You can't actually read my text, so how do you know that each one of those tiny exponents isn't grahams number?
 
  • #75
OrangeDog said:
You can't actually read my text, so how do you know that each one of those tiny exponents isn't grahams number?

If you hit "QUOTE", you can see what you wrote.
 
  • #76
Lies
 
  • #77
OrangeDog said:
no you cant
...Yes... you can...
 
  • #78
more lies
 
  • #79
Code: 
[QUOTE="OrangeDog, post: 5423766, member: 584341"]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP][SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP]

divided by .0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]2[SUP]3[SUP][SUP]2[/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/QUOTE]
 
  • #80
In either case, if you used Graham's number, you needed to specify its usage.
 
  • #81
I guess someone doesn't like trolls.
 
  • #82
I do actually, especially when they fail.
 
  • #83
How about, a googolplex "factorialed" a googolplex number of times?

e.g., 3 "factorialed" two times would be (3!)!, or 6! or 720
 
  • #84
jfizzix said:
How about, a googolplex "factorialed" a googolplex number of times?

e.g., 3 "factorialed" two times would be (3!)!, or 6! or 720

Can't beat Graham.
 
  • #85
wouldn't it take more than 200 characters to properly explain how Graham's number works?
 
  • #86
OrangeDog said:
Micromass takes Graham very seriously.

Aren't you in awe at the hugeness of this number??
 
  • #87
jfizzix said:
wouldn't it take more than 200 characters to properly explain how Graham's number works?

I guess it would. But I allowed referencing to outside sources for explanations.
 
  • #88
micromass said:
Can't beat Graham.
GrahamGraham
 
  • #89
Graham's number is the most terrifying number I've seen, and that's why I love it. No amount of googolplexes anyone strings together will even come close to the might that is Graham's number. If ##G## is Graham's number, every number theory textbook ought to start out by saying "Let ##\infty = G##..."
 
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Likes micromass
  • #90
Maybe we can tighten up the competition to see what's the biggest number we can write with five characters without allowing outside references

e.g.,

9^99!
 
  • #91
jfizzix said:
Maybe we can tighten up the competition to see what's the biggest number we can write with five characters without allowing outside references

e.g.,

9^99!

Then it should be stated clearly what is allowed and what not.
 
  • #92
micromass said:
Then it should be stated clearly what is allowed and what not.

I'd use the same rules as in your original post, but with a 5 character limit instead
 
  • #93
jfizzix said:
I'd use the same rules as in your original post, but with a 5 character limit instead

Sure, but what operations do you consider standard? Obviously numbers 0-9 are allowed (base 10), +, -, *, /, !, what else?
 
  • #94
micromass said:
Sure, but what operations do you consider standard? Obviously numbers 0-9 are allowed (base 10), +, -, *, /, !, what else?
^
 
  • #95
jfizzix said:
^

9^9! seems to be the largest I can think of then
 
  • #96
micromass said:
9^9! seems to be the largest I can think of then
I had to look up what !, was, but from Wolfram Mathworld, 9! = 9*7*5*3*1, which would be less than 9!
 
  • #97
jfizzix said:
I had to look up what !, was, but from Wolfram Mathworld, 9! = 9*7*5*3*1, which would be less than 9!

I just meant the factorial of a factorial really. I severely dislike the (admittedly) standard notation 9! = 9*7*5*3*1.
 
  • #98
ggggG
 
  • #99
mrspeedybob said:
ggggG

Okay now that is large.
 
  • #101
In 5 characters, using only standard operations, and obeying the standard order of operations (thus sometimes requiring parentheses!), I think the best you can do is

(9!)!
 
  • #102
I don't care about Graham cracker's number! I just like googol! :partytime:
 
  • #103
I agree with jfizzix
 
  • #104
The following may seem similar to Berry:

Code: 
The largest number for which any human will ever write a formula or algorithm in the past and future history of the Earth

But, because it doesn't contain the negation of the Berry/Russell version, it is perfectly well-defined and non-paradoxical. It's just that we'd have to wait for the destruction of the Earth for somebody to compute it.

If I put some Knuth arrows at the end of it (there were some characters to spare), it would become self-referential and paradoxical.
 
  • #105
andrewkirk said:
Code: 
The largest number for which any human will ever write a formula or algorithm in the past and future history of the Earth

Someone could express Rayo's[/PLAIN] number [itex]\text{Rayo}(10^{100})[/itex] on Mars, and then you lose ... :wink:

Code: 
The smallest number bigger than any finite number named by an expression in the language of set theory with a googol symbols or less.
 
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