I am sincere, but never wanted you to weigh or do anything with any sympathy in the first place, hence repeating over and over the truism “Arguments either hold or don’t hold completely irrespective of their author and anyone’s emotions.”
You chose not to anyway, so good. We can continue discussing the actual content of the thread and finally bring an end to this whole ad hom charade of bringing in personal issues, emotions and political persuasion.
Not my method.
My method:
Sequentially multiply the terms:
1st term in set one multiplied by 1st term in second one = 1
1st term in set one multiplied by 2nd term in second set = 1
1st term in set one multiplied by 3rd term in second set = 1
which would go on infinitely to get you (1+1+1+…) as you add each result - no need to add James’ extra “+1” to give the illusion of a finite end to an infinite, endless sequence.
We could pretend the sequence reaches an end or just skip at any point to the next stage of:
2nd term in set one multiplied by 1st term in second one = 1
2nd term in set one multiplied by 2nd term in second set = 1
2nd term in set one multiplied by 3rd term in second set = 1
and so on, but this would also continue you on the same infinite addition (1+1+1+…) however you structure your approach.
Now, I actually predicted this wording could be misconstrued by somebody who wanted to misread it, so I clarified as much in my next post on the topic:
Perhaps I should have added the bold and underline when I originally posted it, just to be sure, but it appears you were determined to miss this too.
See all those n terms with subscripts?
They’re the result of simplying like-terms, which in the case of (1+1)(1+1) could have you representing (1+1+1+1) as (2+2), but they’re all like-terms so you might as well fully combine like-terms and write (4) by what your example demonstrates, and both your example and mine would be equally correct, and in the case of (1+1+1+…)(1+1+1+…) you could also represent the result as either (n₁1+n₂1+n₃1+…) OR (1+1+1+…) and pretend the former is “a different order of infinity” or “deeper” than the latter, but in both finite and infinite cases they are just different representations of the same thing, one with some simplification and one without. As with the finite example, the representation does not affect the actual result nor does it affect the same failure to get a result because it infinitely diverges away from one.
But you know what, fuck it. Taking blame is the only language you understand that translates to “commitment” to having my mistakes pointed out if and when they are made, so I’ll take full responsibility for my misleading wording making you think I made a 3rd grade elementary school mistake.
I shouldn’t have even tried to back up my wording with quotes and demonstrations to prove the truth, because now you’ll think I’m trying to dodge the truth because I’m dodging an opportunity to lose face in the wake of one of your accusations.
I would like to point out that providing proof to prove truth is not making excuses to dodge the truth, and the more losing of face is not lessening the degree to which you’re dodging truth, but I am becoming increasingly aware that too many of my words are being wasted trying to manage your hunger to slander and debase me to “prove my commitment” rather than simply asking:
“Did you make this mistake? There is a chance you didn’t and I misread, but the way I read it brought to my attention the possibility that you did.”
I will try to lead by example, and hope you respond in kind.
So, I apologise for making you think you had to point out a 3rd grade elementary school mistake. It’s my fault entirely. To continue this reformed approach, I hope it is to your liking:
I will endeavour to help keep this tangent as brief as possible, please accept any incompetence on my behalf should I fail to live up to your polite request.
You found the issue with your first objection, so we can move straight to the second objection:
The someone you say “would still have to leave from the infinite hotel” would always have another room to “leap frog” to, because it is infinite - this is the intention behind the analogy. There is no "last person in the hotel who would get “boosted out a window” for the same reason you realised about your first objection. There is no “all of the infinity of rooms”, because would imply the encompassing of the “unencompassable”.
I will refrain from addressing your accusations of dumb as this is unproductive.
You are correct that you can’t add an inch to the end of an already infinite rope because it has no end.
You could cut the rope and move it apart to add an inch, because there is no end of the rope to bump up against any edge any more than there was before you cut it.
I humbly request you re-evaluate your analysis of both the hotel and rope paradoxes. You can be assured I will offer no ill will if you do. I would politely request in return you do not insist I have been making mistakes before respectfully asking and gracefully receiving explanation either for against any possible mistakes of mine, which I am sure are highly likely.
Ecmandu I also humbly request you do the same.