Transfinite number - Wikipedia
In mathematics, transfinite numbers or infinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers.
Transfinite number | Cantor’s theory, cardinality, infinity ...
Transfinite number, denotation of the size of an infinite collection of objects. Comparison of certain infinite collections suggests that they have different sizes even though they are all infinite. For example, the sets of integers, rational numbers, and real numbers are all infinite; but each is.
Transfinite Number -- from Wolfram MathWorld
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 ...
What is the difference between "infinite" and "transfinite"?
2020年6月6日 · It is used in a couple fixed phrases: "transfinite induction" and "transfinite recursion", which refer to induction or recursion that is indexed by a general well-ordered set (or more generally, a set with a well-founded relation) rather than just ordinary induction on the natural numbers.
Transfinite Number - an overview | ScienceDirect Topics
The whole of transfinite number theory, and indeed the whole of set theory, begins with the study by Cantor (in connection with problems on the convergence of trigonometric series) of the notion of derived set D(A) of a subset A of R: D(A) is the …
Aleph-null | Definition, Transfinite Numbers, Infinity ...
aleph-null (ℵ0), in mathematics, the cardinality of the infinite set of natural numbers {1, 2, 3, …}. The cardinality, or cardinal number, of a set is the number of elements of a set.
Note (b) for Implications for Mathematics and Its Foundations ...
Transfinite numbers. For most mathematical purposes it is quite adequate just to have a single notion of infinity, usually denoted ∞. But as Georg Cantor began to emphasize in the 1870s, it is possible to distinguish different levels of infinity.