अंतहीन,

transfinite's Usage Examples:

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

starting with the open subsets of X {\displaystyle X} , and transfinitely iterating the operations of complementation and wellordered union.

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

replacement in an essential way, in order to iterate the powerset axiom transfinitely often.

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

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

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

A transfinite cardinal number is used to describe the size of an infinitely large set, while a transfinite.

The least such ordinal is ε0 (pronounced epsilon nought or epsilon zero), which can be viewed as the "limit" obtained by transfinite.

class), is called transfinite induction.

It is possible to iterate this construction transfinitely: given an ordinal α, define a new theory by adding an equivalence relation.

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

obtained by starting with the open subsets of X {\displaystyle X} , and transfinitely iterating the operations of complementation and wellordered union.