Difference between revisions of "Enumeration problem"
From Encyclopedia of Mathematics
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| − | An [[Algorithmic problem|algorithmic problem]] in which one has to construct an algorithm that enumerates | + | <!-- |
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| + | $#C+1 = 10 : ~/encyclopedia/old_files/data/E035/E.0305820 Enumeration problem | ||
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| + | An [[Algorithmic problem|algorithmic problem]] in which one has to construct an algorithm that enumerates $ A $ | ||
| + | for a given set $ A $, | ||
| + | i.e. an algorithm $ \mathfrak A $ | ||
| + | that is applicable to any natural number, that converts it to an element of $ A $ | ||
| + | and such that any element of $ A $ | ||
| + | is obtained by applying $ \mathfrak A $ | ||
| + | to some natural number; in other words, $ A = \{ {\mathfrak A ( i) } : {i \in \mathbf N } \} $. | ||
| + | The enumeration problem for a set $ A $ | ||
| + | is solvable (i.e. such an $ \mathfrak A $ | ||
| + | exists) if and only if $ A $ | ||
| + | is a non-empty [[Enumerable set|enumerable set]]. | ||
Latest revision as of 19:37, 5 June 2020
An algorithmic problem in which one has to construct an algorithm that enumerates $ A $
for a given set $ A $,
i.e. an algorithm $ \mathfrak A $
that is applicable to any natural number, that converts it to an element of $ A $
and such that any element of $ A $
is obtained by applying $ \mathfrak A $
to some natural number; in other words, $ A = \{ {\mathfrak A ( i) } : {i \in \mathbf N } \} $.
The enumeration problem for a set $ A $
is solvable (i.e. such an $ \mathfrak A $
exists) if and only if $ A $
is a non-empty enumerable set.
How to Cite This Entry:
Enumeration problem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Enumeration_problem&oldid=15389
Enumeration problem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Enumeration_problem&oldid=15389
This article was adapted from an original article by V.E. Plisko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article