We have 1999 for the game today. Using all four digits each time, one of each and no other digits at all, you form expressions for consecutive numbers from one up. Any arithmetical signs may be used, except the summation and factorial symbols. Don't forget the root symbol, indices (exponents), and decimals.
For example 1 ^ 999 is a solution for 1. The limit without a break in continuity seems to be 46. Can you do better?
Try also 1137 with limit 94,
and 1688 with limit 100.