Aha! I think I've got it: This rules out that you understand the language and refuse to speak it. You genuinely don't speak the language of math. Okay...
A lot of the stuff you're saying has no meaning to me. The way my mind works, words are just words, so telling me what something is called just gets f...
To slice a pizza into equal slices, try a pizza cutter. Ten paragraphs of nonsense gibberish can be refuted with one kitchen appliance. To most people...
The former has no attribution. The latter says "powered by Oxford" (OUP). I personally was granting that maybe he had one of those ancient analog thin...
I found it on some random russian vocabulary site: (https://slovar-vocab.com/english/fundamental-vocab/number-6810737.html) (ETA: Unhiding this link)....
Sort of. The current definition you have for it has both these properties. You're missing the point. You're trying to apply PoSR in a particular way. ...
Wrong. I have. Also, Banno has: ...using your own dictionary. And your dictionary has, as demonstrated by Banno. Your problem is that you don't unders...
You're going in circles. 1 is one of the possible things that sum can be. Pause for a second and think about this; otherwise this could continue forev...
Okay, so that sum is 50 units. You can only say that if you're literally talking about that 50 unit thing, because: Yes, and 0+0+0... can be equal to ...
It's undefined! :wink: No, it's not arbitrary. It's just infinitely non-specific. That sum genuinely is sometimes 1 inch, sometimes a light year, some...
So you're talking about 0.111...? Then @"Pfhorrest"'s post applies: There is no "at infinity" here though. Every term here is a finite number; there's...
.999... is an infinite string of 9's. There's no problem with that per se. We don't have to say "at infinity"... it's an infinite string of 9's. We ad...
MU, you're pretending here to be making an argument about .999... = 1: A, therefore B, where A is .999... = 1, and B is some rambling about equivalenc...
That's true for all finite x. But you need it to be true for an infinite x. To see the problem, here's a "troll proof" that infinity is finite. 1. 1 i...
But I note that your OED definition talks about values referring to the same particular quantity. And I note that you've chosen of your own will in th...
You should be aware of something about me personally related to that... I'm incredibly patient. Don't ever feel you have to reply to me "timely"... in...
Okay, I think I got it (incidentally, c=k here, right?), but the same objection applies. You still can't apply theorem 1, because you still can't name...
I'm going to take a stab at your confusion then. Here is the full form of the inequality: 1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024 > 1024+1...
You keep handwaving through the same argument's flaw. You have an inequality that's true for term 10: 0.1111111111b > 1024+1024+1024+1024+1024+1024+10...
Your latex is garbled... let me generalize and math this for you. For any positive integral x, no matter how large: \displaystyle\sum_{i=1}^{x}{2^i} <...
What are you talking about? At the 1024th term on the left, we're adding 1024 terms... in binary point, 0.1, 0.01, 0.001, ... , 0.00...001 (with 1 in ...
So that's 10 terms. What happens at the 1024th term? Your left sum is 0.111....11 with 1024 1 bits in binary. Your right sum is 1. Is 0.111...11 with ...
...and you'll find the inequality always breaks down for some number of terms, and all terms after that. In fact, you can cheat... whatever positive i...
dubious. Take x=10^9. I happen to know off the top of my head the left hand side goes below 1/10^9 at term 30 (because I work with computers). So in b...
Here's what I read is going on. You want to talk about an "actual sum" in a meaningful sense, outside of the provided definition. You intuit that it m...
I realize that, but there's no "actual sum" to speak of outside of this definition. In principle I could give an intuitive argument for why .999...=1 ...
You're all over the place here. You have a definition of number that refers to a value (read the newer version of OED; cf to definition 1b of your rev...
So instead of arguing "there are two names for a thing therefore there are two things", which is a red herring, you're just arguing "there are two nam...
It looks to go beyond this. Not only is 0.111... not a number, but there's no such thing as squares, because dimensions are incommensurable (@"tim woo...
What do you mean "If that's the case, then"? There seems to be an implicit assumption that every thing should have exactly one name. Who exactly is ma...
Given that the sum is by definition the limit, then by definition it's the same. You keep tripping over this same point. Apparently not... see the und...
That begs the question of what the heck you mean when you're talking about an infinite sum. Mathematicians regularly compute what they mean by it. It'...
An infinite sum is defined because the mathematics community defined it; same as "twelve" is defined because English speakers defined it. ...that's a ...
Your use of the word "physical" is ambiguous. The controversy is based on your favorite interpretation of quantum mechanics (see Sean Carroll's "The M...
Ah, I think I understand. This is a language barrier. In the language spoken by the mathematics community, .999... represents the same particular quan...
You answered only half of the question... the half about your knowing that it's not any nameable number. What about the other half... how do you know ...
How do you know it's infinity and not, say, an octillion? So if you want to be conservative, just say what you're talking about... "the number of coun...
Well there's a 9 in place 1, a 9 in place 2, and 9 in place 3, and so on... There's a 9 in place 20, a 9 in place 4 billion... apparently, there's a 9...
Ah, but you're forgetting the "falsity indemnification clause": ...if you could. But, if you could, you still won't falsify the theory. You'd merely h...
To get a more meaningful answer, I think we need a more meaningful question. In pursuit of this, can you explain why it's obvious to you that there's ...
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