Neither 0 nor 1 are irrational numbers. So Doom is not necessarily an irrational number. There is a maximum length of all Doom programs in all languages. There

Neither 0 nor 1 are irrational numbers. So Doom is not necessarily an irrational number. There is a maximum length of all Doom programs in all languages. Therefore, if I understand your definition correctly, Doom is always finite and hence not irrational. That the length of the set is unknown is irrelevant - we don't know how many books there are in the world, but we know that it is a finite number. Not knowing what fraction represents Doom is very different from saying there is no such fraction.