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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...

defined the transfinite ordinal numbers and transformed the infinite indices into ordinals by replacing ∞ with ω, the first transfinite ordinal number. Cantor...

Transfinite may refer to: Transfinite number, a number larger than all finite numbers, yet not absolutely infinite Transfinite induction, an extension...

Transfinite induction is an extension of mathematical induction to well-ordered sets, for example to sets of ordinal numbers or cardinal numbers. Its...

where ω is a transfinite number greater than all integers and ε is an infinitesimal greater than 0 but less than any positive real number. Moreover, the...

general, but all its elements do.) Beth number Gimel function Regular cardinal Infinity Transfinite number Ordinal number In older mathematics books, the letter...

numbers are a certain sequence of infinite cardinal numbers (also known as transfinite numbers), conventionally written ℶ 0 , ℶ 1 , ℶ 2 , ℶ 3 , … {\displaystyle...

function F at a finite number of distinct points, these methods match F at a non-denumerable (transfinite) number of points. Transfinite interpolation is similar...

published a book about his new set theory, introducing, among other things, transfinite numbers and formulating the continuum hypothesis. In the 1960s, Abraham...

interest, a fact he was well aware of. Originally, Cantor's theory of transfinite numbers was regarded as counter-intuitive – even shocking. This caused...

number line. Aleph null Suslin's problem Transfinite number Weisstein, Eric W. "Continuum". mathworld.wolfram.com. Retrieved 2020-08-12. "Transfinite...

879–90. doi:10.1137/0513062. Erdos, P.; Gillis, J. (2009). "Note on the Transfinite Diameter". Journal of the London Mathematical Society. s1-12 (3): 185...

Philip Jourdain (ed.). Contributions to the Founding of the Theory of Transfinite Numbers. New York: Dover. ISBN 978-0-486-60045-1. Kurt Von Fritz (1945)...

cardinal number. This cardinal number is called ℵ 0 {\displaystyle \aleph _{0}} , aleph-null. He called the cardinal numbers of infinite sets transfinite cardinal...

number Algebraic number Transcendental number Hypercomplex number Transfinite number Indefinite and fictitious numbers Mean Weighted mean Median Mode Range...

"Zur Einführung der transfiniten Zahlen" [On the Introduction of the Transfinite Numbers]. Acta Litterarum AC Scientiarum Ragiae Universitatis Hungaricae...

Transcomputational problem – Class of computational problems Transfinite number – Number that is larger than all finite numbers Zeno machine – Hypothetical...

{\displaystyle \aleph _{0}} (the cardinal number of the infinite set of integers 1, 2, ...), the smallest cardinal transfinite number. The Jains also defined a whole...

{c}}=\beth _{2}} (beth two) Cardinal characteristic of the continuum "Transfinite number | mathematics". Encyclopedia Britannica. Retrieved 2020-08-12. Weisstein...

well-ordered set that represents the result of the operation or by using transfinite recursion. Cantor normal form provides a standardized way of writing...