I have tried to understand Cantors ideas of infinity, but they still don't make sense to me. If you use the mathematical concept of sets to investigate something like this - a 'value' that can't be written because it has no end - then surely the size of the set is what you are evaluating ? How does changing 'size' to 'order' suddenly make a comparison of individual component s result in something different from size ? There seems to be a fundamental breakdown of logic. I don't mind that at all in mathematical terms. The square root of -1 is essentially illogical, but the reasoning behind it is solid. I love the very concept of complex numbers. But different sizes/orders of infinity seems plain crazy unless 'orders' describes rate of growth in terms of an individual comparison of members of the set. I honestly find it difficult, though it may be because I'm stupid, to understand how such a comparison of members can lead to a conclusion that one type of infinity is bigger than another. There seems to be an unwarrented assumption of an end point that makes no sense in terms of infinity. Infinity seems to be an absolute platonic concept. It just seems plain wrong to convert that concept into a relative one by cutting corners. Pure maths seems beautiful to me - Cantors infinities seem ugly. What is it that I'm missing here ?