Your entire response is misguided. The limit is not describing a point in the shape. If it were, it would be an empty concept; the limit would just be...
From this: That does not follow. 1 is closer to 0 than 2 is, despite the infinite number of points between 0 and 1. I assume by off the scale you mean...
I mean that the future state is a function of the current state, as opposed to fatalism, where the current state is irrelevant to the future state. Wh...
Almost; I'm talking about arbitrarily large but finite amounts of paint. And the only point here is that it's not really surprising this "outside" can...
Determinism and fatalism aren't the same thing. An event that is fated will happen regardless of what occurs. An event that is determined happens beca...
You seem to be imagining a hypothetical number "so big that" 1/x dips below 0. This sounds like speculative fantasy to me. Your reasoning that it dips...
But that is really what's going on at 6:20; the ? there is the ? symbol of the upper limit of the integral, and it is a sentinel; a placeholder meanin...
I'm open to suggestions, but all I'm after here is a description of the space and the object. This is related to the conversation. This came up severa...
I don't see the original paradox; a square foot of area has no meaningful volume. But the same exact questions arise in the finite scenarios. "If it's...
...is there? Back to "intuitive paint" based on real paint, 1 cubic foot of paint can paint 3000 square feet of wall. With that in mind, we can constr...
And the lazier definition of it typically given, such as the one in the video, is that we start with the curve 1/x starting at x=1 and rotate it about...
Nothing you described justifies a concern about the length of tasks. The spatial form is given by Cartesian coordinates with three axes at right angle...
What do you mean this has nothing to do with algebraic geometry?: Gabriel's horn is the algebraic variety defined by the polynomial z^2+y^2=(1/x)^2 st...
Yes. But the subject is the paradox of Gabriel's horn; it's literally the title of this thread. Gabriel's horn is an object defined using algebraic ge...
I can see that you're equivocating. You're confusing "limit" as a method with "limit" as a point beyond which you don't go. The phrase "all the finite...
So to Barondan, I'm quoting these other people for emphasis. There's a generic tendency to equate predictability of choice to lack of choice; but ther...
But you didn't understand it. Yes, but the method is integration. But that is not the method; that is just a shortcut. The method is to apply a limit....
It's right there under your nose and you can't see it. You read: \lim_\limits{x \rightarrow \infty}{\frac{1}{x}} = 0 ...as "saying 1/infinity equals 0...
At this point, it's just denial, and you're unqualified to continue this discussion with. Hardly surprising, given this is the same exact thing you fa...
Wrong. The video used limits (and integrals, which are built off of limits). Limits don't round off to zero. Here's how a limit works: \lim_\limits{x ...
Wrong. You're only confusing yourself here. I haven't specified any rules for paint at all, much less different rules for the inside and outside. Rath...
You're kind of mixing two things in here. Imagine a mathematical bag; inside the bag, we'll put all finite numbers. All of them, mind you, but only th...
See? You don't even know what you're discussing! That is what we're discussing. You made a claim that there's some number, you call it "whatever the l...
You've got this backwards. I have 400 square feet of wall coated with 1/3000th of a foot of paint. How much paint is that? Well, given that the entire...
It depends on what you mean by paint. If filling the inside means the inside is painted, then there's no positive minimal thickness of paint required ...
The questioning of the shape's volume is only said to be problematic because the questioner thinks that the questioner knows what he is talking about....
No, the reason for the appearance of a paradox is that the shape has finite volume and infinite area; that those are two completely different kinds of...
Pathetic ad hominem attempt. There's obviously a difference between avoiding people and vaccinating them, so either you're dense beyond reason or you'...
Just a quick interjection... this statement suggests to me two things: (1) a non-repetitive robot is conscious, (2) a non-repetitive robot is incredib...
^^-- This. You're comparing here a "brain" and a "conscious brain". Let's backtrack: ...this follows unless you're committing an amphiboly between 1 a...
Sure, but a running laptop is physically different than a laptop in sleep mode. But I'm not claiming you have to show that. This was just another exam...
Not quite sure that works TMF. Which is simpler... a running laptop, or a laptop in sleep mode? The answer is kind of a matter of taste, but it also d...
Or, we could practice social distancing. Your pathetic attempts to mock has the problem that the people in Oklahoma that you moved to Arizona still ex...
Nonsense. Here's why. Again, that's a "you" problem. See below. I'd rather not. You see, your problem throughout this ordeal is that you keep assuming...
The following is based on a model that just makes sense to me. For discussion purposes I'll make a distinction between "physical" continuity and "iden...
That sounds like a "you" problem to me. Wrong. The answer, which has been given to you before, only needs a single word: Distance. But is that what yo...
No, Roger, this one of those "my opinion versus your opinion" things that isn't really about opinions. By saying we disagree over the CDC's usage of "...
No, it's an example of a straw man. Person to person does not mean respiratory systems are directly connected. A person to person conversation doesn't...
You wrote: Stop right there. This is a mis-attribution. Here's the full text as it appeared in my post: ...note that this comes from the the CDC gloss...
Let's review, again: My program runs until simulated eradication. 80%/95% scenarios are "sufficient proportion of a population" being immune (underlin...
Roger, I wrote a program demonstrating the effect. I pasted pieces of the program here. I showed you a running video. You started crazily asserting th...
I suggest that your frustration is that I don't agree with something you think is obvious. But I suggest you're not thinking about the situation becau...
We're going in circles. This is the flaw in your theory that makes this ridiculous: ...and those are your specific words. Joe, John are in the same en...
Nope. It's a pretty direct interpretation of your words. Of course it could be true that we need to divide. But you just ruled out what would make tha...
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