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

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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.
 
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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
 
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?
 
micromass said:
Sure, but what operations do you consider standard? Obviously numbers 0-9 are allowed (base 10), +, -, *, /, !, what else?
^
 
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!
 
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.
 
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!)!
 
I don't care about Graham cracker's number! I just like googol! :partytime:
 
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.
 
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.
 
Last edited by a moderator:
Code: 
Graham's number < googology.wikia.com/wiki/TREE(3) < googology.wikia.com/wiki/SCG(13)

You didn't say anything about links! :biggrin:

BIG FOOT: [itex]\text{FOOT}^{10}(10^{100})[/itex] is of course much bigger, but I guess it's disqualified ...
 
Python: 
def FindGraham(s):
    if 'G' in s or 'g' in s:
        return True
    return False

print FindGraham("***")

where *** I put your string, guess now ; the result was false..
by a small modification I even got your character count:
870

Maybe you can fool the eye but not the PC...
 
Code: 
bit.ly/1RFruCp
bit.ly/1OtaqP9
b(x)=busy beaver function
f=BIGFOOT
v(x)=b(f) recursions of b
r(x)=v(f) recursions of v
z(x)=r(f) recursions of r

11 in base z(f)
 
Last edited:
Code: 
G=Graham's Number
G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G[G]G
 
I think there should be a time limit to the contest too. Otherwise people just continue nesting things together.
Also I really can't wait to see how micromass is going to judge which of the numbers given in this thread is bigger!
 
Vanadium 50 said:
How about 7, only with a font size of 9.999 x 10^92?

You did ask for the largest number, and not the number of greatest possible magnitude.:devil:

In the same spirit:

Code: 
[itex]9.\overline{9}[/itex] is the largest (widest) number, as it has an infinite amount of characters to display
 
jack action said:
In the same spirit:

Code: 
[itex]9.\overline{9}[/itex] is the largest (widest) number, as it has an infinite amount of characters to display

So is ##10.\overline{0}##
The ##0##'s are left out for convenience but really should be there.
 
Patrick_Hutecker said:
int y=100000000;
for(x=0;x<-1;x++)
{
y=y*y
}
(never said we could use code)
Since you initialize x to zero, the condition in the for-loop will be false and it will not run your statement.
 
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ah that too

i'm convinced the true winner in this is some perl one liner though, busy beaver be damned