Recursive Definition Of A Set
TOPICS
Recursive Fix
A prepare 
of integers is said to be recursive if there is a total recursive function 
such that 
for 
and 
for 
. Any recursive set is also recursively enumerable.
Finite sets, sets with finite complements, the odd numbers, and the prime number numbers are all examples of recursive sets. The union and intersection of two recursive sets are themselves recursive, equally is the complement of a recursive fix.
Run into also
Recursively Enumerable Set, Recursively Undecidable
This entry contributed by Alex Sakharov (author's link)
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References
Davis, M. Computability and Unsolvability. New York: Dover 1982. Rogers, H. Theory of Recursive Functions and Effective Computability. Cambridge, MA: MIT Press, 1987.
Referenced on Wolfram|Alpha
Recursive Set
Cite this as:
Sakharov, Alex. "Recursive Set." From MathWorld--A Wolfram Spider web Resources, created by Eric Due west. Weisstein. https://mathworld.wolfram.com/RecursiveSet.html
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