1 = 0,99........ - Printable Version +- Frictional Games Forum (read-only) (https://www.frictionalgames.com/forum) +-- Forum: Frictional Games (https://www.frictionalgames.com/forum/forum-3.html) +--- Forum: Off-Topic (https://www.frictionalgames.com/forum/forum-16.html) +--- Thread: 1 = 0,99........ (/thread-18660.html) |
RE: 1 = 0,99........ - Ghieri - 10-07-2012 Quote: Because we have no way of measuring numbers that small at this point inI think you misunderstand, "infinitely small", "infinite", etc are not actual numbers. You can measure numbers. You cannot count to infinity, or measure infinite anything. There is no countable distance between .99~ and 1. It is not that we cannot measure infinity "Yet", it's that infinity is immeasurable by nature. It only exists because theoretically, there is no natural upper limit of numbers. An infinitely small number is not an actual number, because you can continuously divide the number and it will only get smaller and smaller. It does not, by definition, have a value, because you cannot reach the value, or plug it into an equation. It's on the same level as "undefined". Something that exists in mathematics as a way to tell the mathematician they are doing something wrong. Does that make sense? RE: 1 = 0,99........ - Bridge - 10-07-2012 (10-07-2012, 06:48 PM)Aldighieri Wrote:I know. But if a number is "nothing" it is 0.Quote: Because we have no way of measuring numbers that small at this point inI think you misunderstand, "infinitely small", "infinite", etc are not actual numbers. You can measure numbers. You cannot count to infinity, or measure infinite anything. There is no countable distance between .99~ and 1. It is not that we cannot measure infinity "Yet", it's that infinity is immeasurable by nature. It only exists because theoretically, there is no natural upper limit of numbers. 0.00 ... 01 is not zero and yet we have no way of ascertaining its exact value. It's not necessarily infinite, just too small to calculate. Does that make sense? That's all I'm trying to say. Saying it is "nothing" is ignorant and lazy. We have not yet discovered the real "building block" of matter, and yet no reputable scientist would ever dream of saying it was "nothing". Just because it is too small to measure today does not mean it doesn't exist. RE: 1 = 0,99........ - Ghieri - 10-07-2012 Quote: Saying it is "nothing" is ignorant and lazy.Yet the worlds most prominent Mathematicians accept it as fact. Quote: It's not necessarily infinite, just too small to calculate.It's not "too small to calculate" it's "so small it doesn't have a value" Let me explain it this way: Quote: 0.00 ... 01The number of 0's in front of that one are infinite, meaning there are infinite number of zeros, meaning the value can only possibly be resolved as 0. It is not larger than zero, because when running it through calculations, we never reach that last digit. RE: 1 = 0,99........ - Your Computer - 10-07-2012 (10-07-2012, 07:21 PM)Aldighieri Wrote: The number of 0's in front of that one are infinite, meaning there are infinite number of zeros, meaning the value can only possibly be resolved as 0. It is not larger than zero, because when running it through calculations, we never reach that last digit. Is that to say that prominent mathematicians fail at logic or that you aren't a mathematician? For how can you end an "infinite" with "01" and still call it "infinite"? And how can you end an "infinite" with "9" and still call it "infinite"? In order for the equation to work you have to assume that "infinite" or "..." is measurable. Thankfully, "..." doesn't necessarily mean "infinite," in which case 0.99...9 != 1. RE: 1 = 0,99........ - Ghieri - 10-07-2012 Quote: For how can you end an "infinite" with "01" and still call it "infinite"?We are talking about infinitely small numbers, which have to have their "last" digit as 1. My point is that the infinite number of zeroes never reach that point. Therefore, infinitely small. Quote: Thankfully, "..." doesn't necessarily mean "infinite," in which case 0.99...9 != 1.We are not talking about measurably small numbers, so "..." does not equal a finite number of places in this case. If "..." were a finite number of places then I would agree. But it isn't. Quote:Is that to say that prominent mathematicians fail at logic or that you aren't a mathematician?I'm not really sure what I did that put a stick up your ass, but whatever it is probably isn't relevant to the discussion. Anyways, there are several mathematical proofs on the topic: Quote:n = .99~ Quote:1/9 = .11111~ Quote:More here. So while it seems counter intuitive. It is mathematically solid. RE: 1 = 0,99........ - Bridge - 10-07-2012 (10-07-2012, 08:20 PM)Aldighieri Wrote: So while it seems counter intuitive. It is mathematically solid.Because you assume 0.00 … 01 is "infinitely small". I assure you, if you actually used the real number that is being represented, you would not get the solution "1=0.9~". It's like saying: 1/inf x + 1 = 1 0 + 1 = 1 1/inf x = 0 Nobody can say this isn't valid because the number is not calculable and therefore the solution unknowable. 1 divided an infinite amount of times is also an infinitesimal (perhaps even the same number), but it is most certainly not zero. This is an assumption that the solution needs in order to work. It's a loss of data, no matter how much you say it isn't because it "never reaches the last digit" (now there's an absurd mathematical concept for you). RE: 1 = 0,99........ - BAndrew - 10-07-2012 (10-07-2012, 05:08 PM)Bridge Wrote:I already told that this is not an assumption. It is archimedean property.Quote:lim n->nf {0.00 … 01} (n-1) …Quote:AllI didn't make any assumptions. RE: 1 = 0,99........ - Your Computer - 10-07-2012 (10-07-2012, 08:20 PM)Aldighieri Wrote: We are talking about infinitely small numbers, which have to have their "last" digit as 1. My point is that the infinite number of zeroes never reach that point. Therefore, infinitely small. Then any value with "..." is self-invalidated. If you can never reach 01 in 0.00...01 or 9 in 0.99...9, then you can never subtract from it, never add to it, etc. To say that i can is an assumption without evidence--or, more precisely, an assumption contrary to contrary evidence. Quote:We are not talking about measurably small numbers, so "..." does not equal a finite number of places in this case. If "..." were a finite number of places then I would agree. But it isn't. Would you say 1 is measurable? If so, then you are claiming that a measurable number equals a non-measurable number. Quote:I'm not really sure what I did that put a stick up your ass, but whatever it is probably isn't relevant to the discussion. Words on paper have no emotion, neither do words on a screen. Quote: It's not just counter-intuitive, it's illogical. Look at the following example: Line 1: n = .99~ Line 2: 10n = 9.99~ Line 3: 10n-n = 9n Line 4: 9n = 9 Line 5: n = 1 In order for line 3 to lead to line 4 i would have to assume that n is equal to 1. However, line 1 shows that it is equal to 0.99~. Likewise, evidence that n is equal to 1 has not yet been shown. In other words, i have to commit multiple logical fallacies to reach line 5. Of course, if we were to have divided 10 from 10n, therefore making n = .99~, we'd be back at line 1. Likewise, therefore, i would have proven that n cannot be anything but 0.99~, therefore 0.99~ can never equal 1. RE: 1 = 0,99........ - BAndrew - 10-07-2012 (10-07-2012, 09:33 PM)Your Computer Wrote: It's not just counter-intuitive, it's illogical.No it doesn't. You have 10x - x which is equal to 9x. You are probably refering to 9n = 9 which is indeed a mistake as we don't know n = 1(that's it if you don't accept that 9,99... - 0,9999 = 9). See the proof with the limits which is mathematically accepted. RE: 1 = 0,99........ - Ghieri - 10-07-2012 Quote: In order for line 3 to lead to line 4 i would have to assume that n is equal to 1. We know 9n = 9 because 10(.99~)-(.99~) = 9.99~ - .99~ = 9 and 10-1 = 9. Therefore n=9/9 = 1. Quote: It's not just counter-intuitive, it's illogical....except I mathematically proved it. You're welcome to try counter proof but I held up my burden. |