Last Updated：2025/11/22
(mathematics) The theorem which states that any partition of a finite set of n elements into m (< n) subsets (allowing empty subsets) must include a subset with two or more elements; any of certain reformulations concerning the partition of infinite sets where the cardinality of the unpartitioned set exceeds that of the partition (so there is no one-to-one correspondence).
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pigeonhole principle
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Source Word
pigeonhole principle
Noun
countable
uncountable
(mathematics)
The
theorem
which
states
that
any
partition
of
a
finite
set
of
n
elements
into
m
(<
n)
subsets
(allowing
empty
subsets)
must
include
a
subset
with
two
or
more
elements;
any
of
certain
reformulations
concerning
the
partition
of
infinite
sets
where
the
cardinality
of
the
unpartitioned
set
exceeds
that
of
the
partition
(so
there
is
no
one-to-one
correspondence).
Japanese Meaning
鳩の巣原理：有限集合の n 個の要素を m 個（m < n）の部分集合（空の部分集合も許す）に分割すると、必ず2つ以上の要素を含む部分集合が存在するという定理。また、無限集合に対しては、分割前の集合の濃度が分割後の集合群の濃度を上回ることから、ある種の再定式化がなされる。
Sense（1）
(mathematics)
The
theorem
which
states
that
any
partition
of
a
finite
set
of
n
elements
into
m
(<
n)
subsets
(allowing
empty
subsets)
must
include
a
subset
with
two
or
more
elements;
any
of
certain
reformulations
concerning
the
partition
of
infinite
sets
where
the
cardinality
of
the
unpartitioned
set
exceeds
that
of
the
partition
(so
there
is
no
one-to-one
correspondence).
（ plural ）
