-
Transfinite may
refer to:
Transfinite number, a
number larger than all
finite numbers, yet not
absolutely infinite Transfinite induction, an extension...
-
importance of well-ordering is
justified by the
possibility of
applying transfinite induction,
which says, essentially, that any
property that p****es on...
- 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 induction is an
extension of
mathematical induction to well-ordered sets, for
example to sets of
ordinal numbers or
cardinal numbers. 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...
- soon
became known as Cantor's theorem.
Cantor developed a
theory of
transfinite numbers,
called cardinals and ordinals,
which extended the arithmetic...
- interest, a fact he was well
aware of. Originally, Cantor's
theory of
transfinite numbers was
regarded as counter-intuitive – even shocking. This caused...
-
ordinal has a rank
equal to itself. The sets in V are
divided into the
transfinite hierarchy Vα ,
called the ****ulative hierarchy,
based on
their rank....
- P(m))\implies P(n).}
Transfinite induction is the same,
replacing natural numbers by the
elements of a well-ordered set. Often, a
proof by
transfinite induction...
- In set theory, a tree is a
partially ordered set ( T , < ) {\displaystyle (T,<)} such that for each t ∈ T {\displaystyle t\in T} , the set { s ∈ T : s...
