This relation-number is the ordinal number corresponding to n; let it be symbolized by it.
The ordinal number is the class whose sole member is the null relation - that is, the relation which never holds between any pair of entities.
That first discovered is known as Burali-Forti's contradiction,' and consists in the proof that there both is and is not a greatest infinite ordinal number.
Where a number is expressed in terms of various denominations, a cardinal number usually begins with the largest denomination, and an ordinal number with the smallest.
The definition of the ordinal number requires some little ingenuity owing to the fact that no serial relation can have a field whose cardinal number is 1; but we must omit here the explanation of the process.