If I remember correctly, it has to do with rational numbers from one to infinity being countable infinite and the real numbers between 0 and 1 being uncountable infinite. The trick to the proof comes with being able to count rational numbers from smallest to largest (easy to think about with integers but even with rational numbers it's just integers in the numerator and integers in the denominator so just assign a count to the numerator first and the next count to the denomator and it works). for real numbers if you try to count from one number to the next, there will ALWAYS be an number in between those that you missed and should have counted. blew my brain when the professor showed the proof in class.