最終更新日：2024/08/04
(set theory) A demonstration of a surprising property of infinite sets. Some positive integers are squares while others are not; therefore, all the numbers, including both squares and non-squares, must be more numerous than just the squares; yet for every square there is exactly one positive number that is its square root, and for every number there is exactly one square; hence, there cannot be more of one than of the other.
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Galileo's paradox
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元となった辞書の項目
Galileo's paradox
name
(set
theory)
A
demonstration
of
a
surprising
property
of
infinite
sets.
Some
positive
integers
are
squares
while
others
are
not;
therefore,
all
the
numbers,
including
both
squares
and
non-squares,
must
be
more
numerous
than
just
the
squares;
yet
for
every
square
there
is
exactly
one
positive
number
that
is
its
square
root,
and
for
every
number
there
is
exactly
one
square;
hence,
there
cannot
be
more
of
one
than
of
the
other.
意味（1）
(set
theory)
A
demonstration
of
a
surprising
property
of
infinite
sets.
Some
positive
integers
are
squares
while
others
are
not;
therefore,
all
the
numbers,
including
both
squares
and
non-squares,
must
be
more
numerous
than
just
the
squares;
yet
for
every
square
there
is
exactly
one
positive
number
that
is
its
square
root,
and
for
every
number
there
is
exactly
one
square;
hence,
there
cannot
be
more
of
one
than
of
the
other.
