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

>>8657295
The latter, certainly.

Why does it matter?

>>8657300
why does anything matter?

>>8657304
Because some things exist and some things are just abstractions that might not have any real use.

>>8657308
How do we know what exists and doesn't?

>>8657310
wtf I believe in unicorns now

>>8657311
Not on earth, doesn't mean they don't exist anywhere else in the infinite universe

who is the girl in the picture?

>>8657295
If a>b,

a^b < b^a

>>8657295
A(googol^graham,googol^graham)

>>8657789
10>1
therefore
10^1<1^10 or
10<1

brainlet

>>8657295
Well, my dick is quite large, does it mean something to you?

>>8657789
if a>b>1, then b^a>a^b
if b<a<1, then a^b > b^a

>>8657295
-1/12

>>8657819
Also if a=b then b=a

>>8657789
3>2

2^3 > 3^2

???

>>8657830
>Also if a=b then b=a
I'm going to need to see your working for that.

>>8657819
3, 2.
3>2, 2^3=8<3^2=9. Brainlet

>>8657746
Her name is Graham.

>>8657295
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.

>>8657319
>infinite
lol

>>8657846
I'd google her

>>8657789
This is not true when a and b are less than e.

>>8657872
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.

>>8658004
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.

>>8658042
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?

>>8657789
>>8657793
>>8657819
>>8657833
>>8657845
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.

>>8658097
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.