In the context of combinatorial game theory, particularly in the study of games like Nim, a "nimber" is a value that represents the outcome of a game position. A nimber is defined as a non-negative integer that can be associated with game positions.
The statement "0 is a rational nimber" refers to the fact that the nimber value of zero is a rational number. It is also the simplest nimber, representing a position in which the player to move has no legal moves and thus loses the game. The set of nimbers includes all non-negative integers, and since 0 is a non-negative integer, it is indeed a rational nimber.
In summary, 0 is a rational nimber because:
- It is a non-negative integer.
- It signifies a losing position for the player about to move in a game of Nim.