This is discussion archived from a time before the current discussion method was installed.
Falcon Pain: The concept of an infinite amount being of greater magnitude than another infinite amount is not without merit. For a simple example, while there are an infinite number of integers and an infinite number of odd integers, once you apply any kind of boundary, it becomes apparent that the first set has approximately twice the elements of the second set.
There is a reason why infinity/infinity cannot be determined without using certain tricks of the math trade. The most notable of these is L'Hopital's rule. Of course, these can only be proven in the context of equations that use limits. Basically, calculus.
There is also the argument that most of the power levels that are defined as "infinite" in these examples are probably closer to "too high to bother counting". That said, this is still a trope, but not a mathematically impossible one.
Nornagest: If you'll forgive me geeking out for a moment, the sets of integers and odd integers are of equal "size" insofar as it's possible to measure such things -- that is, it's possible to construct a one-to-one mapping between the sets. However, there are infinite sets that don't map one-to-one to the integers and are therefore considered to have higher cardinality; the most intuitive example is probably the real numbers. The proof is actually fairly straightforward; Google "diagonalization argument".
Eric DVH: Color me astonished. I'll admit I haven't watched more than a few episodes (and I've never read the manga), but how can there NOT be any Dragonball Z examples!?
