Comment by rlanday

> You can move from one float to the next, which is a meaningfull operation on discreet numbers like integers, but not continuous numbers like rational and irrational numbers.

What do you mean by continuous? Obviously if you take a number line and remove either the rational or irrational numbers, you will end up with infinitely many holes.

The thing that makes floating point numbers unique is that, for any given representation, there are actually only finitely many. There’s a largest possible value and a smallest possible value and each number will have gaps on either side of it. I think you meant that the rationals and irrationals are dense (for any two distinct numbers, you can find another number between them), which is also false for floating-point numbers.