obsrvr524 wrote:Did you think we forgot?

No. It's amazing how you don't see the connection here...

Like I just said, the rule doesn't change for how you construct these sums, but what you get differs depending on whether they're sums of a finite or infinite series:

obsrvr524 wrote:To multiply two serialized sums, you take the first number from the first set and multiply it times the entire second set. In James' case, that would have been:

1 x (1+1+1...+1) = infA[1]

This method is fine while "..." is a finite number of "1+1"s. Agree for finites, but disagree for infinites - like I already covered - not because the construction is different, but because what you tend towards defies this [n] structure you're imposing on it. That structure is valid for finites because by definition they have ends to distinguish [n] from [n+1] but infinites by definition do not..

obsrvr524 wrote:Then you take the next number in the first set, do the same thing, and add to the previous solution:

1 x (1+1+1...+1) = infA[2]

infA[1] + infA[2] = 2 * infA

You're distinguishing one endless string of "1+1"s from another during the course of the same summation i.e. imposing a bound: a finitude - to separate an endlessness in the middle of its endlessness.

It's as though you're saying that continuing an endlessness on a new line makes the endlessness different. New steps in the same endless process don't give ends to an endless process.

Again, the method you're using is fine while "..." is a finite number of "1+1"s that justifies a distinction that could be validly represented by the structure of [n] followed by [n+1] and so on.

obsrvr524 wrote:Then you take the next number in the first set, do the same thing, and add to the previous solution:

1 x (1+1+1...+1) = infA[3]

infA[1] + infA[2] + infA[3] = 3 * infA

More of the same.

obsrvr524 wrote:And you keep doing that, in this case infinitely, yielding:

infA[1] + infA[2] + infA[3] + .... = infA * infA = infA^2

More of the same - building contradictory assumptions to produce a contradictory result.

It's like, because you don't understand the basic distinction I'm making in your third grade elementary maths, you don't think I get the elementary maths... even though I keep saying I agree with the elementary maths only for finites. I've been saying all along you're using your intuitions about finites to apply to infinites. But somehow, because I'm showing you something you don't seem to understand, "I'm distracting" from what you understand. So, to you, my explanations of what you don't understand have been attempts to "forget" that we need to stick to your elementary mistakes. When you graduate from third grade elementary maths and eventually get to infinites you'll see the difference (clue: it's in the name!)

The alternative that you're completely missing, that there's something you're missing, is what I've been covering all this time - but it all just completely bypasses you... how are you ever going to grow? At this point you're making it very clear that learning and growing is not your intention. All I can do is continue to try and show you where you're going wrong and put up with the presumption that if someone else is seeing something that isn't covered by your understanding, they either don't understand your understanding or are trying to distract from it. Your lip service to finding presumption "sinful" and understanding infinities is just that: lip service.