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.

>>6
first prove that you haven't left any rationals out. i.e that you can reach to any rational a/b. by the process of bisection along two points. ok. let's try a specific example. starting from the intergers ...,-1,0,1,... and doing your bisection thingy, show that you can reach to 1/17.