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Transfinite Number

Transfinite numbers are one of Cantor's ordinal numbers omega, omega+1, omega+2, ..., omega+omega, omega+omega+1, ... 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 in studying foundational issues (Wolfram 2002, p. 1162).

See also

aleph0, aleph1, Cardinal Number, Continuum, Ordinal Number, Whole Number

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References

Ferreirós, J. "The Transfinite Ordinals and Cantor's Mature Theory." Ch. 8 in Labyrinth of Thought: A History of Set Theory and Its Role in Modern Mathematics. Basel, Switzerland: Birkhäuser, pp. 257-296, 1999.Pappas, T. "Transfinite Numbers." The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, pp. 156-158, 1989.Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, pp. 1162, 2002.Wolfram, S. "Expression Evaluation and Fundamental Physics: Transfinite Evaluation." Sep. 29, 2023. https://writings.stephenwolfram.com/2023/09/expression-evaluation-and-fundamental-physics/#transfinite-evaluation.

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Transfinite Number

Cite this as:

Weisstein, Eric W. "Transfinite Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TransfiniteNumber.html

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