In combinatorial game theory, a "nimber" is an element of the game of Nim, which is a mathematical game where players take turns removing objects from piles. A nimber can be any real number represented in a special way, often in relation to positions in the game.
Rational nimbers are specific types of nimbers for which the values can be expressed as fractions and are associated with certain game configurations. To determine whether -9 is a rational nimber, we consider that the nimber values (or Grundy values), particularly for finite impartial games, can be any real number, and rational numbers are included in this category.
Thus, yes, -9 is a rational nimber. In the context of nim, it represents a position from which one can determine the outcome of a game by applying the principles of nim-sum and other relevant calculations.