Sentence examples for relation number from inspiring English sources

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 $\omega$.

Just as a cardinal number can be defined as a class of similar classes where the similarity is simply equinumerosity, the existence of a one to one mapping between the two classes, a relation number is a class of similar classes which are ordered by some relation.

These 'categorial essences' begin with 'object in general' at the top of the tree, which is then divided at the next level into categories including (as examples) object, state of affairs, property, relation, number, etc. (compare lists 1913/2000, 237 and 1913/1962, 61).

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.

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.

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.

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

Table 1 shows descriptive information-tables or relations, number of registers and attributes-from the databases used in the tests.