- In mathematics,
transfinite numbers or
infinite numbers are
numbers that are "infinite" in the
sense that they are
larger than all
finite numbers. These...
-
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...
-
importance of well-ordering is
justified by the
possibility of
applying transfinite induction,
which says, essentially, that any
property that p****es on...
- members, etc. are nested. Each set in this
hierarchy is ****igned (by
transfinite recursion) an
ordinal number α {\displaystyle \alpha } ,
known as its...
- 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...
-
operator taking X to the set of n
satisfying the formula) can be
iterated transfinitely along any
countable well
ordering starting with any set. ATR0 is equivalent...
- interest, a fact he was well
aware of. Originally, Cantor's
theory of
transfinite numbers was
regarded as counter-intuitive – even shocking. This caused...
-
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...
- can
continue it to
infinite ordinal numbers via
transfinite recursion,
thereby obtaining the
transfinite derived series,
which eventually terminates at...
