Indeed, \(\pi\) is an irrational number, meaning it cannot be expressed as a fraction of two integers. In the context of nimbers and combinatorial game theory, a nimber is a specific kind of number associated with games like Nim, and it is typically defined within the set of non-negative integers and zero.
Since \(\pi\) is not an integer (and is indeed greater than 3) and is also not a rational number, it cannot be represented as a nimber. Nimbers are always represented in a form that corresponds to the concept of impartial games, and they are limited to non-negative integer values.
In essence, while \(\pi\) is a fascinating mathematical constant with many important properties, it does not fall within the category of numbers used in the theory of nimbers or combinatorial games.