transfinite's Usage Examples:

In mathematics, transfinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers, yet not necessarily absolutely.

Such a definition is normally said to be by transfinite recursion.

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

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

The transfinite cardinal numbers, often denoted using the Hebrew symbol ℵ {\displaystyle.

Cantor's theory of transfinite numbers was originally regarded as so counter-intuitive – even shocking –.

operator taking X to the set of n satisfying the formula) can be iterated transfinitely along any countable well ordering starting with any set.

The sets in V are divided into the transfinite hierarchy Vα , called the cumulative hierarchy, based on their rank.

In numerical analysis, transfinite interpolation is a means to construct functions over a planar domain in such a way that they match a given function.

well-ordered set that represents the result of the operation or by using transfinite recursion.

recursive formula for producing a series, one can define a transfinite series by transfinite recursion by defining the series at limit ordinals by A λ.

The surreals also contain all transfinite ordinal numbers; the arithmetic on them is given by the natural operations.

A closely related notion is the transfinite diameter or (logarithmic) capacity of a compact simply connected set.

class), is called transfinite induction.

Proofs by transfinite induction typically.

set theory, a large cardinal property is a certain kind of property of transfinite cardinal numbers.

conclude from the well-ordering theorem that every set is susceptible to transfinite induction, which is considered by mathematicians to be a powerful technique.

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