Those sets are the same kind of infinity in size. They're countably infinite. That also has nothing to do with what we're discussing.

The idea that they might count as different kinds of infinities was just mentioned in passing, and I suspect you're wrong about them being the same kind - maybe you aren't up to speed with the latest developments in mathematics in that area.

It's completely different from saying that infinity is a real number that you can add or multiply by.

It has everything to do with what we're discussing - it's the entire point of the paradox, and your proposed solution (which isn't actually yours, but is being pushed by the priests and must therefore be correct no matter how wrong it is) is to ban the issue from being addressed and claim that avoiding the issue equates to a solution.

Look, you can argue that you're not making a mistake by treating infinity this way all you want, and throw around pejoratives like "calculus priests," but the fact is that you're wrong.

Well, obviously you're right because you're simply right, and never mind what correctly applied reason has to say on the matter.

You argued above that if you can multiply infinity by zero which is wrong--that expression doesn't even make sense in math since infinity can't be multiplied: it's not a number.

If you don't take it to the point where there are an infinite number of chunks, you're actually pushing a granular solution, so you're not succeeding in solving the paradox with a non-granular solution. If you attempt to consider an infinite number of chunks, the maths breaks down and you fail. That's the whole point! You are pushing an infinite number of granular solutions and claiming they aren't granular.

Then you argue that adding infinite numbers of things together leads to an infinite result. That's also wrong, and you can prove that various infinite series converge using calculus/analysis.

No, I point out that any attempt to add up the infinite number of chunks goes wrong because if they're all zero in duration, there's nothing to add up, and if they're all greater than zero you can only get an infinite result (and this is not incorrect maths) - neither are mathematically useful as the whole scale has been lost. The only solutions are granular, and the tricks of calculus have nothing profound to say on the matter whatsoever.

If when you count up the items in a series of numbers such as 1, 2, 3, 4, etc. you get an infinity, what sense does it make to say that if you add up 1 + 1 + 1 + 1 + etc. forever you don't also get an infinity? That is identical to counting the items in the series. You are simply not entitled to pick and choose in such a way as to decide that one of these is valid and the other invalid when they are identical processes.