What's a bigger number? Graham's number^Googol or Googol^Graham's number?

What's a bigger number? Graham's number^Googol or Googol^Graham's number?

The latter, certainly.

Why does it matter?

why does anything matter?

Because some things exist and some things are just abstractions that might not have any real use.

How do we know what exists and doesn't?

wtf I believe in unicorns now

Not on earth, doesn't mean they don't exist anywhere else in the infinite universe

who is the girl in the picture?

9

If a>b,

a^b < b^a

A(googol^graham,googol^graham)

10>1
therefore
10^1

Well, my dick is quite large, does it mean something to you?

if a>b>1, then b^a>a^b
if b

-1/12

Also if a=b then b=a

3>2

2^3 > 3^2

???

>Also if a=b then b=a
I'm going to need to see your working for that.

3, 2.
3>2, 2^3=8

Her name is Graham.

To answer your question directly it would be the latter. A googol is 1.0x10^100 which has an essential definition that can be displayed in a mathematical form. Graham's number, however is almost undefined. Graham's number was proved to have enough digits to fill the currently known universe when written out in the tiniest readable font. Naturally the larger the exponent, in this case, indicates an answer.

>infinite
lol

I'd google her

This is not true when a and b are less than e.

The volume of the universe is only in the order of 10^100 plank units (basically smallest unit defined). The universe is absolutely tiny in comparison to Graham's number. You'd need many layers of nested universes before you could write out the entire number, even if the tiniest "readable" font was the size of a plank volume.

That's the observable universe, not the universe. Its size in Planck units and the number of decimals of Graham's number in base 10 is an arbitrary comparison.

Wikipedia says because we can't observe beyond the observable universe we don't know if the universe is finite or infinite but didn't someone prove the universe is finite?

Let a < b

a^b > b^a if and only if

a > -(b productlog(-(log(b))/b))/(log(b))

Which is true if a,b > e.

Since Graham's number > googol > e, googol^Graham's number is greater.

No one has proved the universe is finite. If anything we should assume its infinite since we know it's flat, homogenous, and isotopic. A finite universe would either require some weird boundary that we can't even conceive of or a weird topology.