Sure, any function T -> U partitions T into |U| subsets. But the case where |U|=2 is special because 2^N is special in being the number of subsets of a set of s

Sure, any function T -> U partitions T into |U| subsets. But the case where |U|=2 is special because 2^N is special in being the number of subsets of a set of size N.