So the logic goes, consider x^x^x^...=2. We have an infinite tower of x's. Now, suppose we group all but the first x as so: x^(x^x^x^..)=2. The number of x's in

So the logic goes, consider x^x^x^...=2. We have an infinite tower of x's. Now, suppose we group all but the first x as so: x^(x^x^x^..)=2. The number of x's in the parenthesis is still infinite (infinity minus 1 is still infinity). We already know by hypothesis that x^x^x^...=2. So we can substitute this in for the term in parenthesis since they are both an infinite tower of x's and get: x^2=2.