to the class. For in that case, the class is similar to the sum of itself and the term
, i.e. to a class having one extra term; so that it has the same number as a class with one extra term, so that if
is this number,
. In this case, we shall also have
, i.e. there will be one-one relations whose domains consist of the whole class and whose converse domains consist of just one term short of the whole class. It can be shown that the cases in which this happens are the same as the apparently more general cases in which some part (short of the whole) can be put into one-one relation with the whole. When this can be done, the correlator by which it is done may be said to "reflect" the whole class into a part of itself; for this reason, such classes will be called "reflexive." Thus:
A "reflexive" class is one which is similar to a proper part of itself. (A "proper part" is a part short of the whole.)