i know that two sets have the same cardinality if there exists a bijective correspondence between them and that a set is countable if there exists a bijective correspondence between that set and the set of natural numbers. My teacher proved the set of integers was countable by listing the positive integers along with 0. Then he said that he could just sandwich the negative integers in between the positive ones so the list would look like 0 -1 1 -2 2 -3 3... and so on. What i'm not very clear on is why my teacher chose to sandwich the negative integers between the positive integers like that. couldn't he just have tacked the negative integers at the end of the list of positive integers?