Given infinite time, can one do infinite tasks an infinite amount of times? How many times can one do infinite tasks in infinite time? One would think the ansewr to that question could not be >1, for that would mean that the tasks must have an end and all of them can eventually be completed (implying that they are finite in number, which we said they are not). Now you must consider this: if you were to pick any member of the set of infinity^infinity, I could always pick a member of the set of infinity with a higher numerical value. Doesn't this mean that infinity always equals infinity multiplied by any number? (right now I'm in pre-calc, and the concept of infinity hasn't been explored much yet, so forgive me if there is something I don't understand) Now with that information, we go back to the original problem, that if infinite tasks can be completed more than once in infinite time, then our assumption that the tasks are infinite in number is contradicted. We said that we should be able to complete infinite tasks in infinite time only once, and no more. But according to the 2nd paragraph, wouldn't completing infinite tasks once be the same as completing infinity^2 tasks? And then wouldn't that be the same as completing infinite tasks infinite times? If so, then there is a contradiction. or is there something I am missing...?