How many numbers can you represent using 4 fours and simple arithmetic symbols like +, -, *, /, ^ , log, etc. Concatenation(44,444) and decimals(4.4) are allowed.
This is how I did for the first few natural numbers.
0 = 4+4-4-4
1 = 44/44
2 = 4/4+4/4
3 = (root of 4)^(root of 4) - 4/4
4 = (root of 4)^(root of 4) +4-4
5 = (root of 4)^(root of 4) + 4/4
6 = (4+4+4)/(root of 4)
7 = 44/4 - 4
8 = 4+4+4-4
9 = 4 + 4 +4/4
10= 4/.4 +4-4
11 = 4/.4 + 4/4
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