Final answer:
To show that the positive even integers are countable, map each natural number to its double, which establishes a one-to-one correspondence.
Step-by-step explanation:
The question asks to show that the set of positive even integers E+={2,4,6,8,...} is a countable set. A set is countable if its elements can be put into a one-to-one correspondence with the set of natural numbers.
For positive even integers, we can define a function f from the set of natural numbers to E+ by mapping every natural number n to 2n. This function is clearly injective (one-to-one) and surjective (onto) since for every even positive integer x, there is a natural number n such that 2n=x. This establishes a one-to-one correspondence between E+ and the set of natural numbers, therefore E+ is countable.