Last Updated：2025/12/19
Sentence
For
not
only
do
the
antinomies
a)
to
e)
disappear
when
we
admit
as
elements
of
sets
only
such
sets,
ordinal
numbers,
and
cardinal
numbers
as
are
bounded
above
by
a
fixed
cardinal
number,
but
we
see
also
that
paradoxes
always
arise
if
we
collect
into
a
set
any
sets,
cardinal
numbers,
or
ordinal
numbers
which
are
not
bounded
above
by
a
fixed
cardinal
number.
Quizzes for review
For not only do the antinomies a) to e) disappear when we admit as elements of sets only such sets, ordinal numbers, and cardinal numbers as are bounded above by a fixed cardinal number, but we see also that paradoxes always arise if we collect into a set any sets, cardinal numbers, or ordinal numbers which are not bounded above by a fixed cardinal number.
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