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...

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

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...

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

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

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

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)...

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

number Negative number, Positive number, Parity (mathematics) Prime number, Composite number Non-standard numbers, including: Infinity, transfinite number...

transfinite 1.  An infinite ordinal or cardinal number (see Transfinite number) 2.  Transfinite induction is induction over ordinals 3.  Transfinite recursion...

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

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

In mathematics, the epsilon numbers are a collection of transfinite numbers whose defining property is that they are fixed points of an exponential map...

{\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...

arithmetic. While ST is silent as to whether there is a maximal type, a transfinite number of types poses no difficulty. These facts, reminiscent of the Peano...

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...

are nested. Each set in this hierarchy is assigned (by transfinite recursion) an ordinal number α {\displaystyle \alpha } , known as its rank. The rank...

can continue it to infinite ordinal numbers via transfinite recursion, thereby obtaining the transfinite derived series, which eventually terminates at...

Transcendental number Transcendental realism Transcendental Students Transcendental theology Transcendentalism Transcendentals Transferable utility Transfinite induction...

concept which has a well-defined formal meaning in some number systems, and may refer to: Transfinite numbers, numbers that are larger than all the finite...

constructing models of set theory by repeating Cohen's forcing method a transfinite number of times. Iterated forcing was introduced by Solovay and Tennenbaum (1971)...

can be thought of as a number that is bigger than any other conceivable or inconceivable quantity, either finite or transfinite. Cantor linked the Absolute...

free number variable n and a free set variable X, seen as the operator taking X to the set of n satisfying the formula) can be iterated transfinitely along...