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Arithmetic sequences.
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Sequences of real numbers.
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What is a sequence
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Bounded sequences.
Definition
3
.
2
.
1
Let
be a sequence.
The sequence
is bounded above if there exists a real number
such that
.
The sequence
is bounded below if there exists a real number
such that
.
The sequence
is bounded if it is bounded above and bounded below.
Example
3
.
2
.
2
Let
for any
.
The sequence
is bounded below:
The sequence
is not bounded above, i.e. for any real positive number
, there exists an
such that
. We have:
Actually, for any
, we have
.
Example
3
.
2
.
3
The sequence whose general term is
is bounded, as everyu sine is greater than or equal to -1 and less than or equal to 1.
Next:
Arithmetic sequences.
Up:
Sequences of real numbers.
Previous:
What is a sequence
Contents
Noah Dana-Picard 2007-12-28