What is larger? Graham's number or Googolplexian? See YouTube or wikipedia for the defination of Graham's number.
A Googol is defined as $10^{100}$.
A Googolplex is defined as $10^{\text{Googol}}$.
A Googolplexian is defined as $10^{\text{Googolplex}}$.
Intuitively, it seems to me that Graham's number is larger (maybe because of it's complex definition).
Can anybody prove this?

Googolplex can be bounded from above like a tower of exponents, so $$10^{10^{100}} < (3^3)^{10^{100}} = 3^{3\times 10^{100}} <3^{10^{101}} < 3^{(3^3)^{101}} = 3^{3^{303}} < 3^{3^{3^{3^3}}}$$ In the last step, we have used the fact that $303$ is much,much smaller than $3^{27}$. Now, take the Googolplexian.We can thus, easily check that,  $$10^{10^{10^{100}}} < (3^3)^{10^{10^{100}}} < 3^{3^{3^{3^{3^3}}}}$$ So, Googolplexian is much smaller than a tower of exponents of $3$'s of length $6$, or in other words Googolplexian is less than $3\uparrow \uparrow6$.(using Knuth's up-arrow notation.)

Now, compare this with just the first layer of Graham's number,i.e., $3\uparrow \uparrow \uparrow \uparrow 3$. Hope it helps.
