listing all finite subsets of natural numbers

Question

is there a computable algorithm which lists all the finite subsets of natural numbers ?... i know that such a set is atleast countable... but can't determine if we can list every such subset in a computable manner .....

the set of all infinite sequences of the subsets of natural numbers is obviously uncomputable

i think this problem should be computable, since any finite set is computable... but i need some sort of proof or reference , any site etc... thanks

Specifically, the easy answer is this one: https://math.stackexchange.com/a/200395/87023 — Chris Culter, Nov 04 '23 at 07:58
@ChrisCulter thanks for the link, this one nails it for me personally - https://math.stackexchange.com/a/200398/1203803 can't believe i didn't think of it at first — , Nov 04 '23 at 08:11

score 2 · Accepted Answer · answered Nov 04 '23 at 07:51

2

The following algorithm lists all finite subsets of natural numbers.

output (empty set)
for n from 0 to infinity:
    for every subset S of {0, ..., n - 1}:
        output (S union {n})

It's easy to see that every finite subset of natural numbers will be output exactly once within finitely many steps.

answered Nov 04 '23 at 07:51

WhatsUp

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so this is exactly this method right - https://math.stackexchange.com/a/200398/1203803 – Nov 04 '23 at 08:09
Yes I think so. – WhatsUp Nov 04 '23 at 08:37

listing all finite subsets of natural numbers

1 Answers1