4 4's puzzle

[tricky77puzzle]

Alright, so here's how the game is played:

You're trying to make as many numbers as possible using 4 4's or less, in an attempt to try to prove an old theory: "You can make any whole number using only four instances of the number four and commonly used mathematical symbols."

So so far, the symbols allowed are:
1. All standard mathematical operators (+-*/)
2. Factorials (n! = n * (n-1) * (n-2) * ... * 2 * 1)
3. Square roots, arbitrary roots (the index is included in the 4 4's)
4. Repeat signs (denoted with an apostrophe ' or grave accent `, ex. 0.3` = 0.33333.....)
5. Exponentiation (denoted with a caret ^, 2^8 = 2*2*2*2*2*2*2*2, 8 2's)
6. Decimals do not require a leading zero. So you could put .4 instead of 0.4.

I'll start:
0 = 4-4
1 = 4/4
2 = sqrt(4)
3 = 4 - 4/4
4 = 4
5 = 4 + 4/4
6 = 4 + sqrt(4)
7 = 4 + 4 - 4/4
8 = 4 + 4
9 = 4 + 4 + 4/4
10 = 4 + 4 + sqrt(4)

And the next person would continue from 11, 12, and so on, and introduce new symbols and explaining them if necessary.