Question 479459
Your post is a little bit of overkill. Simply remember that the set of real numbers is the set of all numbers that you can point to on a number line. The set of rational numbers is the set of all numbers that can be expressed as a ratio of two integers. The set of integers is {...-2,-1,0,1,2,...}. The set of whole numbers is the set of integers greater than or equal to zero. The set of natural numbers is the set of whole numbers, except the number "0." Irrational numbers do not fall into any of these sets (except real numbers, of course), they simply cannot be expressed as a ratio of integers, e.g. sqrt(2) or pi.