Last Updated：2026/01/01
Sentence
The
validity
of
the
principle
of
transfinite
induction
for
well-ordered
sets
enables
us
to
carry
out
proofs
by
transfinite
induction
and
definitions
by
transfinite
induction.
A
proof
by
transfinite
induction
is
a
direct
application
of
the
principle
when
it
is
required
to
show
that
each
element
of
a
well-ordered
set
A
has
a
property
P.
[…]
To
understand
the
method
of
definition
by
transfinite
induction
some
preparation
is
necessary.
Quizzes for review
The validity of the principle of transfinite induction for well-ordered sets enables us to carry out proofs by transfinite induction and definitions by transfinite induction. A proof by transfinite induction is a direct application of the principle when it is required to show that each element of a well-ordered set A has a property P. […] To understand the method of definition by transfinite induction some preparation is necessary.
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