The sleight of collection

An idea from graduate school that I was quite proud of was based on observing different kinds of "1". There is the counted number '1'. There is the ordered 'first'. There is the distance from the zero to one along the real number line. I liked the idea of using the same name for a collection as for the last element of the collection. Thus '{1,2,3}' is identified with '3'. I called this the "sleight of collection" because it is like a sleight of hand whereby some underlying dynamics get captured in the naming of things.