Last Updated：2025/11/26
(mathematical analysis) The lower limit of a sequence of real numbers is the real number which can be found as follows: remove the first term of the sequence in order to obtain the first subsequence.
Then remove the first term of the first subsequence in order to obtain the second subsequence.
Repeat the removal of first terms in order to obtain a third subsequence,
fourth subsequence,
etc. Find the infimum of each of these subsequences, then find the supremum of all of these infimums. This supremum is the lower limit.
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lower limit
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Source Word
lower limit
Noun
(mathematical
analysis)
The
lower
limit
of
a
sequence
of
real
numbers
is
the
real
number
which
can
be
found
as
follows:
remove
the
first
term
of
the
sequence
in
order
to
obtain
the
"first
subsequence."
Then
remove
the
first
term
of
the
first
subsequence
in
order
to
obtain
the
"second
subsequence."
Repeat
the
removal
of
first
terms
in
order
to
obtain
a
"third
subsequence,"
"fourth
subsequence,"
etc.
Find
the
infimum
of
each
of
these
subsequences,
then
find
the
supremum
of
all
of
these
infimums.
This
supremum
is
the
lower
limit.
Japanese Meaning
数学解析において、実数列の各部分列（先頭の項を順次取り除いて得られる各部分列）の下限の集合の上限として定義される値。つまり、その数列の「下極限」または「リミット・ロウアー」として知られる概念です。
Sense（1）
(mathematical
analysis)
The
lower
limit
of
a
sequence
of
real
numbers
is
the
real
number
which
can
be
found
as
follows:
remove
the
first
term
of
the
sequence
in
order
to
obtain
the
"first
subsequence."
Then
remove
the
first
term
of
the
first
subsequence
in
order
to
obtain
the
"second
subsequence."
Repeat
the
removal
of
first
terms
in
order
to
obtain
a
"third
subsequence,"
"fourth
subsequence,"
etc.
Find
the
infimum
of
each
of
these
subsequences,
then
find
the
supremum
of
all
of
these
infimums.
This
supremum
is
the
lower
limit.
（ plural ）
