Last Updated：2025/11/26
(mathematical analysis) The upper 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 supremum of each of these subsequences, then find the infimum of all of these supremums. This infimum is the upper limit.
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upper limit
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Source Word
upper limit
Noun
(mathematical
analysis)
The
upper
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
supremum
of
each
of
these
subsequences,
then
find
the
infimum
of
all
of
these
supremums.
This
infimum
is
the
upper
limit.
Japanese Meaning
（解析学）実数列の各部分列の上限（すなわち、各段階での残りの項の上界）の中で最も低い値、すなわち上極限を示す。
Sense（1）
(mathematical
analysis)
The
upper
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
supremum
of
each
of
these
subsequences,
then
find
the
infimum
of
all
of
these
supremums.
This
infimum
is
the
upper
limit.
（ plural ）
