cardinality love

# cardinality

## Definitions

• 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 one-to-one, one-to-many, many-to-one, or many-to-many.

• n. (mathematics) the number of elements in a set or group (considered as a property of that grouping)

## Etymologies

cardinal +‎ -ity (Wiktionary)

## 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).

A Short Critique of Bradley Monton's Paper

• 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.

The Early Development of Set Theory

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

Vienna Circle

• 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.

KansasCity.com: Front Page

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

Mathematical logic and multiverses

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

Mathematical logic and multiverses

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

Mathematical logic and multiverses

• 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.

Mathematical logic and multiverses

• 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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