Now examine the sum of a rational number Y and an irrational number X the rational number y can be written as y equals A over B where A and B are integers and B does not equal 0 leave the irrational numbers X as X because it can be written as the ratio of two integers let's look at a proof by contradiction in other words were trying to show that x + y is equal to a rational number instead of an irrational number let the sum equal m Over N where M and N are integers in M does not equal 0 the process for rewriting the sum for X is shown