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Given a sequence
, any infinite subset of the sequence forms a subsequence. We formalize this as follows:
Equivalently,
is a subsequence of
if
-
is a sequence of elements of , and
- there is a strictly increasing function
such that
 for all 
Example 1 Let
 and let  be the sequence
Then, the sequence
is a subsequence of  . The subsequence of natural numbers mentioned in the definition is
 and the function
 mentioned above is  .
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"subsequence" is owned by alozano. [ full author list (2) | owner history (1) ]
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(view preamble)
Cross-references: function, natural numbers, strictly increasing, infinite subset, sequence
There are 37 references to this entry.
This is version 3 of subsequence, born on 2002-08-16, modified 2007-06-22.
Object id is 3300, canonical name is Subsequence.
Accessed 5032 times total.
Classification:
| AMS MSC: | 00A05 (General :: General and miscellaneous specific topics :: General mathematics) |
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Pending Errata and Addenda
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