Excerpts below. This is typical. AI: Georg Cantor was a devout Catholic PROMPT: What makes you say cantor was a catholic AI: I apologize for the overs...
AI is amazing. The ability of a program to generate conversational text at such speeds is astounding. It is an incredible intellectual achievement. An...
What aspect of Cantor are you supporting? I'm trying to figure out what you're saying about Cantor and Godel. I'm still wondering what your view is re...
That is great. It proves my point. AIBot gives two versions, both wrong, and both on the same point. (1) Here's the start of AIBot's argument: Suppose...
It's not ruled out that in certain circumstances a chatbot can provide more explanation. But one has to be very very careful. Aside from whatever corr...
What passages do you refer to? / You said Cantor and Godel say "once one sees". I take 'one' to refer to humans, not to a god. But did Cantor or Godel...
I don't know what relationship you have in mind between the quote of @"fishfry" (refuted by me) and the quote of me, especially since neither referenc...
Meanwhile, for a reality check, it would help to know that you recognize that to infer that there are no infinite sets requires not just dropping the ...
I have no objection to the system of extended reals. I explicitly said that it is rigorous. And, of course, it can be useful rotationally (and perhaps...
Yes, I mean the ordinary definition. Your analogy works in my favor. Given that I already have a definition of 'a topology', I can just say 'a topolog...
That is a good one to get back to. Dropping the axiom of infinity does not entail that there is not a set that has all the natural numbers as members....
A confession long overdue. / "I understand the idea that given a property, there is the set of things that have that property (with some restrictions ...
Your question is answered by reading what I posted about that. You skipped what I said about that. Whoa. I did not at all invoke unrestricted comprehe...
(1) It's hyperbole that I "attack" in all cases. Rather, most often I just plainly state the correction. But often when it's a crank who continues to ...
I said that I should not have said 'formally'. Recognizing an error in wording is not a bad thing. I don't blame you if you took my remarks not in the...
I should not have said 'formally'. I meant informal deduction. My point was to contrast informal deduction with "mind's eye" visualization. I reason f...
That was Zeno's scam. He conned people into thinking that Tortoise had just as good a chance as Achilles, then he took people's bets on Tortoise. It's...
That seems well put. I use reason to formally conceive that there are infinite sets. It's easy: I understand the property of being a natural number; a...
What series? A series is an infinite summation, which is the limit of a sequence of finite sums; ordinarily the domain is w, so there is no w-th invol...
The system of extended reals is rigorous. And we can define '-inf' and '+inf' in a way to instantiate the system. Then, one may wish to define such no...
I don't see a need for disagreement here. You can notate as you wish; and I can say why I also use that notation but like to point out that 'inf' is d...
Personally, I don't take the first one as involving the extended reals. I take 'inf' in lim 1/x = 0 as notation that unpacks as: 0 = the limit of the ...
Back to matters at hand: Hopefully you might now at least be beginning to understand the answers to your question: There is the denumerable sequence t...
The quintessential crank* Metaphysician Undercover misquotes me. I didn't post any sentence that begins with "ave". But this is a true sentence I did ...
Bull. You spout misinformation. Then you get explanations and ignore them, evidenced by asking questions that were already answered as you just go rig...
After many posts where I made no personal comments, I have correctly said that the poster is ignorant and confused about mathematics. And that is not ...
That is not pedantic. The formuation you gave is literally very incorrect. I simply offered a correct formulation. For that, you reply petulantly (tho...
It's not pedantic but it is pedagogical. The key idea is sequences. And it is clear and concise to say: The domain is w+1 = wu{w} (or, taking libertie...
You mean the ordering: L u {<-inf n> | n in w} u {<n inf}> | n in w}, where L is the standard ordering on the natural numbers. The formulation you gav...
It's not a quirk. It's odd terminology, as far as I know; and the context here is not just points at infinity but sequences, and sequences are functio...
You can call them whatever you want. (I see that there is a Wikipedia article that does use the terminology though. I don't usually reference the unre...
What's to elaborate? I gave you the definitions of 'the continuum' and 'continuous function'. Meanwhile, a definition of 'a continuum' is not needed i...
Not "extended natural number". Rather the ordinal w+1 = wu{w}. That has been explained to you probably at least five times already. And there is no "p...
Wrong. A series is a certain kind of function. Since it is a function, the range of the function is indexed by the domain of the function. Again, you'...
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