This relation-number is the ordinal number corresponding to n; let it be symbolized by it.
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.
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.