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Rating article for WikiProject Mathematics. Quality: Start / Priority: Mid / Field: foundations (script assisted) |
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::::Another question -- suppose a lookup table is created by picking a million numbers from a random number table, and an algorithm is created that halts only when given an input that is in the lookup table. Would that algorithm determine an r.e. set? [[User:Wanderer57|Wanderer57]] ([[User talk:Wanderer57|talk]]) 15:45, 10 August 2008 (UTC)
:::::Yes. Every finite (or co-finite) set of natural numbers is recursively enumerable. Indeed, they are recursive. [[User:JRSpriggs|JRSpriggs]] ([[User talk:JRSpriggs|talk]]) 16:13, 10 August 2008 (UTC)
Article says:
:* There is an algorithm that enumerates the members of S. That means that its output is simply a list of the members of S: s<sub>1</sub>, s<sub>2</sub>, s<sub>3</sub>, ... . If necessary, this algorithm may run forever.
I have requested discussion at [[talk:algorithm characterizations]] of whether this is a legitimate use of the word "algorithm", which I thought had to produce at most finite output. [[Special:Contributions/66.127.52.47|66.127.52.47]] ([[User talk:66.127.52.47|talk]]) 21:20, 20 March 2010 (UTC)
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