Sentence examples for cardinal number from inspiring English sources

If this condition is valid when restricted to set algebras F of cardinality less than some fixed cardinal number κ, then we say that X has the κ-SVM property.

The symbol ℵ0 (aleph-null) is standard for the cardinal number of N (sets of this cardinality are called denumerable), and ℵ (aleph) is sometimes used for that of the set of real numbers.

The continuum hypothesis asserts that c equals aleph-one, the next cardinal number; that is, no sets exist with cardinality between aleph-null and aleph-one.

In these terms, the continuum hypothesis can be stated as follows: The cardinality of the continuum is the smallest uncountable cardinal number.

A rather direct generalization can be drawn that says that, if a theory has any infinite model, then, for any infinite cardinal number, it has a model of that cardinality.

The cardinality of any set $A$, denoted by $|A|$, is the unique cardinal number that is bijectable with $A$.

By the smallest transfinite cardinal number he meant the cardinal number of any set that can be placed in one-to-one correspondence with the positive integers.

Georg Cantor's continuum hypothesis states that there is no cardinal number between ℵ0 and 2ℵ0.

This is necessary because the cardinal number refers to the first letter of the author's last name.

Then a natural choice for the cardinal number of A is the least ordinal to which A is equivalent.

This is the motivation for defining a cardinal number as an ordinal that is not equivalent to any smaller ordinal.