Relation-number
Relation-number
Dyadic relations R and R’ are said to be similar (or ordinally similar) if there exists a one-one relation S whose domain is the field of R, and whose converse domain is the field of R’, such that, if aSa’ and bSb’ then aRb if and only if a’Rb’ . The relation-number of a dyadic relation may then be defined as the class of relations similar to it — cf. cardinal number.
The relation-number of an ordering relation (see order) is called also an ordinal type or order type.
The notion of a relation-number may be extended in a straightforward way to polyadic relations. — A.C.
Whitehead and Russell, Principia Mathematica, vol. 2.