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

[Borek]

It is insane. As long as we deal with numbers that can be expressed either directly or using logarithmic scales I have no problems comparing orders of magnitude (and guessing which number is larger, or trying to somehow evaluate their values). But I fell so hopelessly lost when it comes to hyperoperations

 

[epenguin]

The product of all the numbers except this one that have been and will be posted on this thread raised to the power of that same number that same number of times.

 

[Borek]

all the numbers except this one that have been and will be posted

No way.

- No references to earlier posts allowed.

But you can take a product only of all numbers that WILL be posted to stay in accordance with the rules

 

[micromass]

But you can take a product only of all numbers that WILL be posted to stay in accordance with the rules

And since I will post $0$, that is not a good idea.

 

[Ben Niehoff]

And since I will post $0$, that is not a good idea.

The product of the factorials of (the absolute values of) all the numbers that will be posted, then. :D

 

[ShayanJ]

The product of the factorials of (the absolute values of) all the numbers that will be posted, then. :D

So I'll post $\infty$!

 

[Ben Niehoff]

A(G,G),

where A is the Ackermann function and G is Graham's number.

 

[mrspeedybob]

A(G,G),

where A is the Ackermann function and G is Graham's number.

Why stop there?

A(A(G,G),A(G,G))

is only 16 characters. If you include definitions...

A=Ackermann function
G=Gram's number
A(A(G,G),A(G,G))

Now it's still only up to 51, so, by expanding on the same idea and being slightly more concise with the explanation you can get...

Ackermann function
Gram's number
G↑↑A(A(A(A(A(A(G,G),A(G,G)),A(A(G,G),A(G,G))),A(A(A(G,G),A(G,G)),A(A(G,G),A(G,G)))),A(A(A(A(G,G),A(G,G)),A(A(G,G),A(G,G))),A(A(A(G,G),A(G,G)),A(A(G,G),A(G,G))))),A(G,G))

Which by my count comes to 200 characters, including spaces.

 

[mrspeedybob]

Or...

Ackermann function
Gram's number
B(n,x)=A performed recursively n times with arguments x. I.E. B(2,3)=A(A(3,3),A(3,3))
C(n,x)=B performed recursively n times with arguments x.
C(C(G,G),C(G,G))

 

[ChrisVer]

f(x)=10^x!
f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(9)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

 

[micromass]

f(x)=10^x!
f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(9)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

This is still dwarfed by Grahams number though...

 

[ChrisVer]

This is still dwarfed by Grahams number though...

maybe... I haven't seen that number...
But if it's big I could try to put it in the f(f(...f(f(G))...)), and in place of 10 in 10^x! : G^x!

 

[mrspeedybob]

maybe... I haven't seen that number...

Fair warning. It'll break your brain.
http://waitbutwhy.com/2014/11/1000000-grahams-number.html

 

[Dembadon]

G^G↑^{G^G}G^G, where G is Graham's number.

 

[micromass]

G^G↑^{G^G}G^G, where G is Graham's number.

I'm afraid that doesn't beat the hugeness of the Ackerman function. https://en.wikipedia.org/wiki/Ackermann_function

 

[Dembadon]

I'm afraid that doesn't beat the hugeness of the Ackerman function. https://en.wikipedia.org/wiki/Ackermann_function

Indeed. So I looked at mrspeedybob's post and cut a few characters out so I could fit in exponents for the arguments of C. Microsoft Word says it's 200 characters exactly including spaces:

Ackermann func.
Graham's #
B(n,x)=A performed recursively n times with args x. I.E. B(2,3)=A(A(3,3),A(3,3))
C(n,x)=B performed recursively n times with args x.
C(C(G^C(G,G),G^C(G,G)),C(G^C(G,G),G^C(G,G)))

 

[nolxiii]

11

 

[CynicusRex]

0

As I think most of the universe is empty space, 0 pretty much sums it all up.
This is probably incorrect on many levels, but I like the idea.

 

[nolxiii]

-1/12

 

[rootone]

∞-1

 

[micromass]

∞-1

In which number system are you working when you say $\infty$ ?

 

[nolxiii]

11

also, to clarify, this number is not written in base ten but in some much larger base size

 

[micromass]

also, to clarify, this number is not written in base ten but in some much larger base size

Then you need to specify the base in your description.

 

[rootone]

In which number system are you working when you say $\infty$ ?

Lets say binary for simplicity, although I do realize that that a computer memory containing the number would require an infinite number of bits.

 

[nolxiii]

no one else specified their base size

 

[micromass]

no one else specified their base size

Do we really need to specify that 100% of humans nowadays work standard in base 10?

 

[micromass]

Lets say binary for simplicity, although I do realize that that a computer memory containing the number would require an infinite number of bits.

But $\infty$ is not a real number. So what kind of number is it? How is it defined?

 

[collinsmark]

For those interested in Graham's number, here is a video about it.

Also, Knuth's[/PLAIN] up-arrow notation is introduced in the video.

 

[ChrisVer]

what would happen in case I write:

lim_[n ->0] 1/n^2

??

 

[micromass]

what would happen in case I write:

lim_[n ->0] 1/n^2

??

Not a real number.