Last Updated：2025/12/01
(mathematics) A theorem in set-theoretic geometry, which states that given a solid ball in three‑dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball.
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Banach-Tarski paradox
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Source Word
Banach-Tarski paradox
Proper noun
(mathematics)
A
theorem
in
set-theoretic
geometry,
which
states
that
given
a
solid
ball
in
three‑dimensional
space,
there
exists
a
decomposition
of
the
ball
into
a
finite
number
of
disjoint
subsets,
which
can
then
be
put
back
together
in
a
different
way
to
yield
two
identical
copies
of
the
original
ball.
Japanese Meaning
集合論的幾何学における定理であり、三次元空間内の球体を有限個の互いに交わらない部分集合に分解し、それらの部分集合を再組み合わせすることにより、元の球体と同一のものを2つ作り出すことができるというパラドックス（逆説）を示す。
Sense（1）
(mathematics)
A
theorem
in
set-theoretic
geometry,
which
states
that
given
a
solid
ball
in
three‑dimensional
space,
there
exists
a
decomposition
of
the
ball
into
a
finite
number
of
disjoint
subsets,
which
can
then
be
put
back
together
in
a
different
way
to
yield
two
identical
copies
of
the
original
ball.
