Last Updated：2025/11/26
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To determine the upper limit of a sequence of real numbers, remove successive initial terms to form tail subsequences, find the supremum of each tail, and then take the infimum of those supremums.
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To determine the upper limit of a sequence of real numbers, remove successive initial terms to form tail subsequences, find the supremum of each tail, and then take the infimum of those supremums.
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Related words
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。
Related Words
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