How real are the real numbers, really?

We usually say that infinity isnt real, but here well see how crucial it is to have one very big infinity for the real world; there is an infinite number of numbers. But why do we need real numbers at all? Arent rational numbers enough? And what about hyperreal numbers? What well see in this video is that discovering or defining the real numbers is what allowed calculus to be made rigourous- and without it, wed need to divide by 0 every time we took a derivative. This video is about the seeming mathematical paradox that arises to get Archilles from A to B (that isnt Zenos paradox!).