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Transfinite number. In mathematics, transfinite numbers or infinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers.
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 f...
- 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 Number. 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.
Transfinite numbers are infinite…but not quite. They are either cardinal numbers or ordinal numbers, and are used to compare the sizes of infinite sets.
Learn the meaning of transfinite, an adjective that describes something that goes beyond or surpasses any finite number, group, or magnitude. See examples of transfinite in sentences and its origin and usage in mathematics.
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.
