Joel Uckelman on Wed, 28 Jul 2010 06:21:24 -0700 (MST) |
[Date Prev] [Date Next] [Thread Prev] [Thread Next] [Date Index] [Thread Index]
Re: [game-lang] Another quick tangential comment about integers and reals |
Thus spake Simon McGregor: > > In regard to rationals and reals, imagine the following: a game is > played by moving points on a board in R2, up to 1 unit's distance at a > time (with the Euclidean metric). We can model this using the > rationals, because rational arithmetic is adequate to determine > whether two points with rational coordinates are within a rational > distance of one another. > > However, suppose that the provably optimal move in some situation is > to move your point as far as possible towards another point. Then (in > general), no move in the rational model is optimal, although there's > an optimal move in the continuous model. Uh-oh! > I don't follow this last bit of reasoning. It seems to imply that there's some real r which is nearer to a target t than any rational q is. If you have a nonstandard model of the reals where you also have infinitessimals, then this could be the case (the move would be t-\epsilon), but not so for the standard reals. -- J. _______________________________________________ game-lang mailing list game-lang@xxxxxxxxx http://lists.ellipsis.cx/mailman/listinfo/game-lang