What do finite, infinite, countable, not countable, countably infinite mean? [duplicate] Ask Question Asked 13 years, 4 months ago Modified 13 years, 4 months ago

Aug 6, 2024 · In such a model, there are sets the model thinks are finite, but which are actually infinite; so there's a distinction between "internally infinite" and "externally infinite."

Feb 3, 2022 · b) Intersection of any finite collection of sets in the family belong to the family. These definitions intrigue me and make me ask the question : What is special about finite vs. infinite sets …

Dec 5, 2015 · Since all finite sets are countable, uncountable sets are all infinite. Per Cantor's theorem, the real numbers are uncountable. Further, since any interval can be put in 1-1 correspondence with …

Sep 25, 2018 · Something has been bothering me recently with regards to compactness in finite vs. infinite dimensional vector spaces. By theorem of compactness in finite dimensional normed space …

Jun 13, 2013 · What familiar and intuitive properties of finite dimensional vector spaces fails in infinite dimensions? For example: In infinite dimensions there are non-continuous linear maps. In infinite …

May 21, 2017 · As @RyanA has commented, the only truly infinite populations are abstract theoretical ones. For practical statistical purposes, it is sometimes feasible to treat a sufficiently large finite …

Here is a paraphrase of the first item in Michael Hoppe's answer: Proper linear subspaces of finite dimensional vector spaces have strictly smaller dimension. (compare e.g. Prove that a set is infinite if …

Mar 9, 2017 · In optimal control, What is infinite horizon problem? What is the difference between finite and infinite horizon? What are their real life examples (finite & infinite)?

Mar 7, 2015 · For an infinite set, its power set and the set of its finite subsets are different sets (they of course agree for finite sets). Finite sets of real numbers always have a maximum (and thus a …