I mean, irrational numbers are maybe "ugly" from a certain perspective, but they are the price we pay for other things that make our life easier. Rational numb

I mean, irrational numbers are maybe "ugly" from a certain perspective, but they are the price we pay for other things that make our life easier. Rational numbers are arguably nice and easy. But if all we have are rational numbers, 2 doesn't have a square root. More in general, our number line has holes, and one of the most fundamental properties of analysis - that every non-empty bounded set has a least upper bound - goes away. We could do away with that (and arguably, irrational numbers don't really exist "in the outside world") but it would make all the calculations so much more complicated.