-
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...
- soon
became known as Cantor's theorem.
Cantor developed a
theory of
transfinite numbers,
called cardinals and ordinals,
which extended the arithmetic...
- 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...
- interest, a fact he was well
aware of. Originally, Cantor's
theory of
transfinite numbers was
regarded as counter-intuitive – even shocking. This caused...
-
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...
- In
mathematical logic, second-order
arithmetic is a
collection of
axiomatic systems that
formalize the
natural numbers and
their subsets. It is an alternative...
- In set theory, a tree is a
partially ordered set (T, <) such that for each t ∈ T, the set {s ∈ T : s < t} is well-ordered by the
relation <. Frequently...
