cardinality

How To Use cardinality In A Sentence

• Indeed, because cardinality is permutation-invariant, every cardinality quantifier is included, including “there are infinitely many”, “there are uncountably many”, and others that are not first-order definable. Logical Constants
• 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. Archive 2009-06-01
• 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
• We understand that sets have a cardinality, that is, that collections have a number associated with them and it doesn't really matter what the members of that set are.
• Dedekind also provided a proof of the Cantor-Bernstein Theorem (that between any two sets which can be embedded into each other one-to-one there exists a bijection, so that they have the same cardinality), another basic result in the modern theory of transfinite cardinals. Dedekind's Contributions to the Foundations of Mathematics
• 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
• 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
• (In the case of a complete theory, the models of different cardinality will be elementarily equivalent, even if they are non-isomorphic). Archive 2009-06-01
• (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
• As for the aleph-null and aleph-one: it was proven that the continuum hypothesis essentially whether the cardinality of real numbers is aleph-one or higher is undecidable in standard set theory, so whether you want to accept it or not, you won’t hit any contradictions. Intelligent Design explained: Part 2 random search - The Panda's Thumb