Two general aspects or uses of maps
1. Sorting of the domain by a property
The abstract sets we are talking about are only little more than numbers, but this little difference is enough to allow them to carry rich structures that numbers cannot carry. In the example of the Chinese restaurant that we discussed in Session 5, I used the word ‘stacking.’ Now I would like to introduce some other words which are often used for the same idea.
For a general map we can say that g gives rise to a sorting of X into B ‘sorts’, or that the map g is a sorting of X by B. (Note that we are speaking of ‘B’ as if it were a number.) Once g is given, every ...