Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. Of a set, the number of elements it contains.
 n. The property of a relationship between a database table and another one, specifying whether it is onetoone, onetomany, manytoone, or manytomany.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. (mathematics) the number of elements in a set or group (considered as a property of that grouping)
Etymologies
Examples

For example, it certainly depends on whether your set of trials is countably infinite or uncountably infinite (in other words the cardinality of your set of trials).

Thus, if you write card (N) = µ 0 (read: aleph sub zero), his theorems justified calling the cardinality of the “second number class” µ 1.

(Newman 1928, 144) To see how this socalled cardinality constraint applies to ramseyfications of theories, note that in Carnap's hands, the nonobservational part of reconstructed theories, their theoretical entities, were represented by “purely logicomathematical entities, e.g. natural numbers, classes of such, classes of classes, etc.”

At recess, one boy, Joshua, used a pointer to illustrate a math concept known as cardinality, by completing place settings on a whiteboard.

One boy, Joshua, used a pointer to illustrate a math concept known as cardinality, by completing place settings on a whiteboard.

Needless to say, general relativity has models which employ the cardinality of the continuum, hence general relativity will possess models of every cardinality.

(In the case of a complete theory, the models of different cardinality will be elementarily equivalent, even if they are nonisomorphic).

The latter entails that any theory which has a model of any infinite cardinality, will have models of all infinite cardinalities.

Models of different cardinality obviously cannot be isomorphic, hence any theory, complete or incomplete, which has at least one model of infinite cardinality, will have a multiverse associated with.

We are talking about the cardinality of the null set here.
None is, none are: Grammar according to Clarkson « Motivated Grammar
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