Irrational numbers cannot exist

Let's look at the number line. You can see -5,-4,-3,-2,-1,0,1,2,3,4 and so on. If you look between 0 and 1 there is going to be a rational number 1/2 exactly in the middle. There is going to be a rational number 1/4 exactly in the middle of 0 and 1/2. You can do this for any two numbers and make the distance between them smaller and smaller.

So you can fill up the whole number line by cutting it in halves. Therefore, the whole number line is made up of rational numbers and irrational numbers cannot exist.

>>10
If there are an infinite number of rational numbers between 1 and 2, then that means that there are no holes. How can there be an infinite number of rational numbers between two numbers and it to have holes? It is impossible and proves that irrational numbers cannot exist.