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In mathematics, transfinite numbers or infinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers. These include the transfinite cardinals, which are cardinal numbers used to quantify the size of infinite sets, and the transfinite ordinals, which are ordinal numbers used to provide an ordering of ...
Jun 6, 2020 · Learn the difference between \"infinite\" and \"transfinite\" numbers, and how they are used in set theory and topology. See answers from experts and users, with references to Cantor's theory and related topics.
- No, there is no such definition. The term "transfinite" is just not used at all as a technical term in modern mathematics. It is used in a couple...
- Infinite simply means "not finite", both in the colloquial sense and in the technical sense (where we first define the term "finite"). There is no...
- When Cantor first outlined his theory of transfinite numbers, he wanted to stress that there are indeed distinct numbers beyond the finite numbers....
- I give another interpretation on the differences between "infinite" and "transfinite". Note that the following propositions involve no Axiom of Cho...
A transfinite number is a symbol for the size of an infinite set, such as the real numbers or the set of all functions involving real numbers. Learn how to compare different transfinite numbers and the continuum hypothesis.
- The Editors of Encyclopaedia Britannica
Transfinite numbers are one of Cantor's ordinal numbers , , , ..., , , ... all of which are "larger" than any whole number . As noted by Cantor in the 1870s, while it is possible to distinguish different levels of infinity, most of the details of this have not been widely used in typical mathematics. However, transfinite numbers can be helpful ...
Transfinite numbers are numbers that help us compare the size of infinite sets, such as the natural numbers and the real numbers.
In mathematics, transfinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers, but not necessarily absolutely infinite. These numbers can be categorized into two types: transfinite cardinals and transfinite ordinals.
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Transfinite induction is an extension of mathematical induction to well-ordered sets, for example to sets of ordinal numbers or cardinal numbers. Its correctness is a theorem of ZFC . [1]
