Alright, let's settle this once and for all."0.999... = 1"What comes after 1? 0.999... and the number that comes "next" have to necessarily be different. If the difference is 0 then it is not the "next" number if it isn't zero then there is a number between it and zero.This means there is no "next" number.What is the difference between 0 and not 0.To say 0.999... = 1 is to say the difference between 0.999... and 1 is 0 but then what is the "next" number after 1/0.999...? It must necessarily be greater than 0 but if it is then the difference between it and zero must be greater than 0.0.999=1 tards can't answer thisThe debate is over.0.999.../=1
>What's the next number?There is no "next number" except in discrete sets, while what you are talking about as numbers is continuous
>>17040292>What comes after 1?2
>>17040293You have not answered anything.If there is no "next" then you can't coherently have a concept of "greater than" or "less than"There is no such thing as a number "greater than zero" since it's existence would necessitate a "number" between it and zero
>>17040293For example. Take any two numbers in a set. If their difference is greater than zero they are not the same, if it's zero they are the same.Take another set with zero and a "different" number.To say there is no "next number" after zero necessitates separation without "difference".This is not possible.
>>17040293
>>17040292>What comes after 1?1.0000.....1
>>17040301Look at the post above yours and answer the question
>>17040303They treated me like a retard when I proposed this a couple years back.
>>17040297>>17040299In mathematically dense sets no two numbers can be directly adjacent to eachother since you can always find a number between the two. > and < can't be defined by successor functions like n+1 or n+0.000...1. To do greater than or less than we have to define "greatness" in terms of distance rather than it coming up after in successor function.
>>17040314>>17040314Does not matter."Distance" has to be either 0 or "greater" than zeroYou can not coherently go from zero to "not zero" without there being a thing that exists "after" zero.There is a thing "after" zero that has Distance from zero greater than zero.YES OR NO.If you answer "yes" you have created "Distance", once there is "Distance" you can partition it.If you answer "No", DISTANCE CAN NOT EXIST.CHOOSE ONE.
>>17040321Can you, non circularly, define what "next" even means in this context?
>>17040326A thing that has "Distance" from zero such that there is "nothing" between it and zero.This "thing" can not exist therefore "Distance" can not exist.The second you claim there is a thing greater than zero that is not zero you necessarily have to have "difference"Once you have "difference" you have to answer what's the "difference" between zero and not zero.WHAT IS THE DIFFERENCE BETWEEN ZERO AND NOT ZERO.
>>17040332>"Distance" from zero such that there is "nothing" between it and zero.Such a concept is explicitly forbidden in the real (and even the rational) number system as a direct consequence of the Axiom of Completeness. Whatever number system you are attempting to evoke here is not the number system under which 0.999...=1 applies and is therefore not relevant to the discussion.QED
>>17040332Not zero is a not a number. If you define not zero then you have your answer. For instance if you define not zero as 0.5 then the next number after 0.999... is 1.5
>>17040303This, but this is actually also just equal to 1
>>17040332>WHAT IS THE DIFFERENCE BETWEEN ZERO AND NOT ZERO.found the virgin
>>17040292Lol what? This doesn’t make sense at all. How does 0.9… being the same number as 1 (by the additive identity 1 - 0.9… = 0) have anything to do with a different number that isn’t equal? This is literally nonsense.
>>17040321NTA but it's easy. Imagine a number line, which you mathfags propose exists. Then there is a continuous spectrum of numbers. You identify, arbitrary, a few of them as integers as 0, 1, 2, etc. You can place some dots on the line to denote these points. You begin at 0. Now, how do you transition along this number line to reach 1? As a matter of fact, 1 is some finite distance away from 0, is it not? Now, you mathfags will also tell me there are as many numbers in the interval (0,1) as there are in (0,infty). What is this number of numbers? Who cares, just label it X and call them literally equivalent. That's what equal and the same means, right? Now put the two number lines (0,1) and (0,infty) stacked, one above the other with the same equal lengths and same labelings of the end points. Again, keep all the integers 0, 1, 2 etc. labeled with dots.In the top line (0,1), it's quite trivial what you see. Only the two end points labeled, let's call that distance 1 cm. In the bottom line, how far away are the dots 0 and 1? You will tell me, formally, zero. That is, a literal, physical distance of 0 cm. The same distance between 0.999... and 1, which you say are formally distance-zero away, and therefore the same number. Thus, 0 and 1 must also be the same number. Right?
>>17040587NTA but this is a thread about how 1 and 0.9… are the same number because 1 - 0.9… = 0 and how this is somehow related to a different number that’s different. Fuck off and start a new thread if you want to talk about distance and measure, or clarify what you think OP’s logic is—how this different number is relevant to the equation in any way.
>>17040593I'll take your aggression as a sign of a concession at that you understand the argument while being incapable of refuting here. Here, let me distill it down for you in green text>if 0.999.. = 1 because 1 - 0.999... = 0 [a distance measure]>then 0 = 1 because 1 - 0 = 0 [a distance measure]in fact, no length of the line drawn (0,infty) can ever produce a non-zero measurable distance between 0 and 1, and therefore 1 - 0 = 0. I mean, you DO claim infinity and infinitesimals have a utility to measurable reality, do you not? Either they're measurable and 0 = 1, or infinities are made up nonsense with no bearing on reality. Pick one. That is, either 0.999.. = 1 is true (and 1 = 0 too) or 0.999... = 1 is not true.
>>17040596>Indian debate syntaxFiltered because you can't read. Fuck off and make a new post about lines and distance somewhere else; it has nothing whatsoever to do with OP.
>>17040596
>>17040605>>17040606Thank you for your responses. This tells me I'm on the right track for proving to people that 0.999... is not equal to 1. I will continue to share this argument in the future here, encouraged by your continued support.
>>17040609human>an apple is a fruit because it's the fruit of a fruit treejeet npc>but ALSO an apple is a fruit because a fruit fairy pooed it on the street instead of the loo>but does a fruit fairy really exist?>therefore an apple isn't a fruit>I will continue to share this argumentkek
>>17040332One of them has a NOT and one does … not
Static Vs. Dynamic Observation.
>>17040587>>17040596The problem in your logic here is that you are scaling your equations by a factor of infinity when you are "proving" 1 = 0. There are infinite numbers between 0 and 1 but not infinite distance. Numbers innately have no distance. Now you can backwards logically "prove" that 1-0 = 0 but only if you first hide infinity somewhere in that equation which makes it erroneous.
>>17040292theyre defined equal chud. trust the math.
>>17040630No, the “logic” problem is that the equality follows simply from 0 being an additive identity and from how integers are defined in decimal notation. “Infinity” has fuck all to do with it.No one needs a magical jeet fairy here. And if you WANT to retrofit a magical jeet fairy into a simple proof, it’s on you to prove 1) that your jeet fairy exists in the first place and 2) that it’s backward compatible to the proof.
>>17040292You do not understand rational numbers.
>>17040735"Magical jeet fairy"what is this schizo even talking about anymore?
