Inspired by the "make 24" thread, but an open-ended version.
This was an annual contest in a magazine here, but it was for obvious reasons discontinued in year 2K. The idea is to use the four numbers to come up with 0, 1, 2, ... . 1998 was a special year for me for more reasons than one, so we'll go with that. If someone has another special year in our lifetimes, by all means go for it.
* basic math expressions + - x : are ok
* roots are ok, but nth root requires the use of the number n.
* Square root is ok and can be expressed without a 2.
* numbers can be raised as exponent for powers.
* numbers may not be glued together, e.g. 1 9 -> 19
* the original order need be retained.
* expressions requiring letters or words, such as LCD or LCM, are out.
* expressions requiring a symbol, such as factorial, are in.
To get started,
0 = 1 x (9 - 9) x 8
1 = 1 ^ 9 ^ 9 ^8
2 = 1 + (9 / 9) ^ 8
3 = 1 x sqrt(9) x (9 - 8)
etc. There are multiple ways for the first few, but it gets harder soon enough.
How far can one get?