Sentence examples for relation numbers from inspiring English sources

Ordinal numbers are the relation numbers of well-ordered classes.

Ordinal numbers are a special case of relation numbers.

All of the properties of the arithmetic of ordinal numbers are derived from the more general arithmetic of relation numbers.

On the other hand addition of ordinals, and indeed relation numbers in general, is associative, that is, $\alphaa + \beta) + \gamma = \alpha + (\beta + \gamma)$, which is proved with certain restrictions in *174.

The class of real numbers, Θ, is defined in Volume III of Principia Mathematica at *310.01 as consisting of "Dedekindian series" of rational numbers, which are in turn relation numbers of "ratios" of natural numbers.

Whitehead and Russell follow the account of real numbers as Dedekind cuts of the rational numbers, and only differ from more standard developments of the numbers in contemporary set theory by treating rational numbers as relation numbers of a certain sort, rather than ordered pairs of and integers (the "numerator" and "denominator").

The first infinite ordinal $\omega$ is the relation number of the well-ordered classes similar to $1 , 2 3, \ldots$ etc.

The sum $1 + \omega$ will be the relation number of ordered classes which result from adding one element at the beginning of the ordering, say $0 , 1 2, 3, \ldots$ etc., which has the same ordinal number $\omega$.

The first concerns the nature of the relata, or "objects", whose relations numbers are supposed to mirror.

Refusing to give up until I had confirmation that this was, in fact, just a test, I called the White Plains public relations number.

To give another, it is in Principia that we find the first detailed development of a generalized version of Cantor's transfinite ordinals, which the authors call "relation-numbers".