# Talk:Index finite lists of positive integers

## Sets or lists?

"It is known that the set of finite lists of positive integers is countable"
I know that the set of finite sets of positive integers is countable.
What is a list? If it is something like the example Perl is using "12 11 0 7 9 15 15 5 7 13 5 5", which is not a set, are these are countable?--Nigel Galloway (talk) 12:57, 8 September 2018 (UTC)

Yes.
Any list of finite integers may be represented as a set of finite integers:
A non-zero integer at position n in a list may be represented as the n-th odd prime raised to the power of the absolute value of that integer (with the result taking the sign of that integer).
A zero in position n in the list may be represented as 2 to the n-th power.
As these values are distinct this set representation will have the same number of elements as the original list.
As this set representation is a set of finite numbers, any constraint on the cardinality of the set must also hold for the original list. —Rdm (talk) 19:02, 8 September 2018 (UTC)