Last Updated：2025/12/02
(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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Source Word
Galileo's paradox
Proper noun
(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.
Japanese Meaning
無限集合の意外な性質を示す逆説。具体的には、正の整数全体と、その平方数との間に一対一対応が存在するという事実を示し、部分集合であっても元の集合と同じ濃度を持つというパラドックス。 / ガリレオの逆説。集合論における無限集合の性質に注目し、数字の平方数との対応関係から、一見矛盾する性質が明らかになる現象を表す。
Sense（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.
