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.
Let `a` be a rational number and `b` be an irrational number,assume that the sum is rational. 1.a +b =c Where a and c are rational and b is irrational. 2.b=c-a Subtracting the same number a from each...
The rational numbers form a field. In particular, the sum or difference of two rational numbers is rational. (This is easy to check directly). Suppose now that a + b = c, with a rational and c...