Is there a "largest function"? In one of my classes, the professor asked about what we think the largest function was. Many thought perhaps ${e^x}^{e^x}$, but I thought about $n!$

When I talk about a "largest function", I mean the function that increases the quickest. 

The professor asked about a function larger than $n!$ to which I responded, $2n!$

Although snarky in nature, it is technically true. 

So my question is this:


  What is the "largest function" if we define "largest" as being "increases the quickest". A parent function is what we need, as it prevents someone like myself from putting a larger coefficient before the function.
There are many large functions, e.g. $e^n$, $n!$ etc.

And you might know that $e^n$ grows faster than $n^k$ for any $k\geq 1$.

But there are other interesting functions, e.g. the Busy Beaver function. It asymtotically grows faster than any computable function. That means you cannot even write a computer program that produces a faster growing function.

The nice thing is: The busy beaver function is well-defined, but not computable:)! This function really gives an upper bound for the growth of computable functions (e.g., it grows much faster than any function that just contains hyperoperators or the TREE function).

edit: Of course, there are more and even faster growing functions.
I'm just saying, the function that I think is the LARGEST ar aka the one that increases the value of the number is, what I invented, is Pxn("number").That kinda makes in infifnite because how it works for example if I took $1$, it would give me $\pi$, but if I take $3$, that means take every single number of $\pi$ and multiply it by $3$ so $``3.14"$ would be $``6.312"$.
So there you go, bye (I wrote this and I'm 9yr old)