The sum of a rational and an irrational number is always irrational. Here is a brief proof: Let a be a rational number and b be an irrational number, and c = a + b their sum. By way of contradiction,...
No, but you can add an infinite amount of rational numbers by way of Tailor Series and get an irrational number. That is actually how numbers like "Pi" and "e" are derived.
The way in which the binary functions, addition and multiplication, are defined on the set of rational numbers ensures that the set is closed under these two operations.
The set of rational numbers includes all whole numbers, so SOME rational numbers will also be whole number. But not all rational numbers are whole numbers. So, as a rule, no, rational numbers are not...