cardinalities

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

Archive 2009-06-01 Gordon McCabe 2009

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 Gordon McCabe 2009

“The monkeys can only represent cardinalities in an approximate way.”

HERE’S LOOKING AT EUCLID Alex Bellos 2010

“The monkeys can only represent cardinalities in an approximate way.”

HERE’S LOOKING AT EUCLID Alex Bellos 2010

“The monkeys can only represent cardinalities in an approximate way.”

HERE’S LOOKING AT EUCLID Alex Bellos 2010

At the same time, the Löwenheim-Skolem theorem says that every first-order formal theory that has at least one model with an infinite domain, must have models with domains of all infinite cardinalities.

Philosophy of Mathematics Horsten, Leon 2007

Rejection of Different Infinite Cardinalities: Given the non-existence of infinite mathematical extensions, Wittgenstein rejects the standard interpretation of Cantor's diagonal proof as a proof of infinite sets of greater and lesser cardinalities.

Wittgenstein's Philosophy of Mathematics Rodych, Victor 2007

Given Wittgenstein's rejection of infinite mathematical extensions, he adopts finitistic, constructive views on mathematical quantification, mathematical decidability, the nature of real numbers, and Cantor's diagonal proof of the existence of infinite sets of greater cardinalities.

Wittgenstein's Philosophy of Mathematics Rodych, Victor 2007

It is not apparent at first that there might be infinite sets of different cardinalities, but once this becomes clear, it follows quickly that the structure so described is rich indeed.

Set Theory Jech, Thomas 2002

It may be possible to construct sets '' A '' and '' B '' for which there is no way to compare their cardinalities: there is no injective function from '' A '' into

Conservapedia - Recent changes [en] Sunda62 2010