- #1
nomadreid
Gold Member
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Given the two standard definitions
(1) A computable set is a set for which there is an algorithm which terminates after a finite amount of time and correctly decides whether or not a given number belongs to the set.
(2) A computable number is a number which can be approximated to any degree of accuracy by a computable function
I am tempted to say that a computable number is one that corresponds to a computable set, but
(a) I am not sure this is correct, and
(b) even if it is correct, I am not sure what "corresponds to" would mean. There are ways to make any subset of the natural numbers correspond to a real number, but I am not sure whether these would be appropriate.
Thanks.
(1) A computable set is a set for which there is an algorithm which terminates after a finite amount of time and correctly decides whether or not a given number belongs to the set.
(2) A computable number is a number which can be approximated to any degree of accuracy by a computable function
I am tempted to say that a computable number is one that corresponds to a computable set, but
(a) I am not sure this is correct, and
(b) even if it is correct, I am not sure what "corresponds to" would mean. There are ways to make any subset of the natural numbers correspond to a real number, but I am not sure whether these would be appropriate.
Thanks.