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

[micromass]

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.

 

[jfizzix]

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

 

[micromass]

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?

 

[jfizzix]

Sure, but what operations do you consider standard? Obviously numbers 0-9 are allowed (base 10), +, -, *, /, !, what else?

^

 

[micromass]

^

9^9! seems to be the largest I can think of then

 

[jfizzix]

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!

 

[micromass]

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.

 

[mrspeedybob]

g_gggG

 

[axmls]

g_gggG

Okay now that is large.

 

[jfizzix]

Graham's number is too dam high

 

[Ben Niehoff]

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!)!

 

[TheQuietOne]

I don't care about Graham cracker's number! I just like googol!

 

[TheQuietOne]

I agree with jfizzix

 

[andrewkirk]

The following may seem similar to Berry:

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.

 

[DevilsAvocado]

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 \text{Rayo}(10^{100}) on Mars, and then you lose ...

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

 

[DevilsAvocado]

Graham's number < googology.wikia.com/wiki/TREE(3) < googology.wikia.com/wiki/SCG(13)

You didn't say anything about links!

BIG FOOT: \text{FOOT}^{10}(10^{100}) is of course much bigger, but I guess it's disqualified ...

 

[ChrisVer]

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...

 

[nolxiii]

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)

 

[Isaac0427]

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

 

[micromass]

What does [G] mean?

 

[Isaac0427]

What does [G] mean?

I figured hyperoperation was allowed without explanation as it goes directly with Knuth's notation.

https://en.wikipedia.org/wiki/Knuth's_up-arrow_notation#Generalizations

 

[ShayanJ]

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!

 

[jack action]

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.

In the same spirit:

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

 

[micromass]

In the same spirit:

[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]

int y=100000000;
for(x=0;x<-1;x++)
{
y=y*y
}
(never said we could use code)

 

[nolxiii]

y is 32 bit int?

 

[Dembadon]

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.

 

[nolxiii]

ah that too

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

 

[m k]

While true n = n + 1

 

[micromass]

While true n = n + 1

Doesn't terminate so not a valid number.