Question

An infinite set is countable if and only if it is possible to list the elements of the set in a sequence (indexed by the positive integers).

true or false

Answer 1

An infinite set is countable if it is possible to list all its elements in a sequence indexed by the positive integers.

Step-by-step explanation:

A set is countable if and only if its elements can be listed in a sequence indexed by the positive integers. This means that each element in the set can be assigned a unique positive integer as its index. An infinite set is countable if it is possible to list all its elements in a sequence. For example, the set of natural numbers is countable because we can list them as 1, 2, 3, 4, ... and assign each number a unique positive integer index. Therefore, the statement is true.