Dammit saw through it. Well ummmRabid Toilet said:
Ok fine ill stop trying to dispove it. I already know it is true.
Poll: 0.999... = 1
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Ok fine ill stop trying to dispove it. I already know it is true.
It exists in math. N-dimensional lattices exist in math, but you can't construct one in your mind. Just because something may be incomprehensible, does not mean it doesn't exist. 0.(9) is a number. Some of its representations are infinite. There are no processes there, they just are.Lyx said:
Math is axiomatic and absolute. If a system or a theory says something works in a certain way, then it just does, within that system. There is no intuition, there is nothing to comprehend, there is only Math and its laws, as defined by the System's Postulates. If you deny an axiom and substitute your own, you create a new system with a new ruleset. If you do it as a part of a proof, the proof is invalid in the original system and therefore irrelevant.
Sufficiently advanced math is indistinguishable from magic.
Then you disagree with the question, not the result (since the answer of an incoherent question cannot be true or false). Assuming you take the view that this is an erroneous question, you should probably realize that you are, in the end, arguing that all real numbers are only processes (Values having multiple representations stems from the nature of constructing representations of real numbers. So you can, for any real number, create a number system that forces you to conclude that the values are processes). As soon as you take such a view, you either have to abandon a notion of equality altogether or you have to say that they're equal. So nothing is really ever gained.Lyx said:
More simply, .999... is very definitely a number. The fact that you can't conceive of it as a number is a problem with your own understanding of mathematics. To say that one can't mean anything else is downright false, since I certainly mean a number when I say .999...
You're also verging on deeper epistemological questions, which would derail this thread and which I don't really want to try to deal with given a naive audience on the internet. Suffice it to say that claiming that infinity doesn't "exist" as anything other than a process is an extremely problematic view to hold.
That is part of my dislike for maths and how it is abused to for real-world modelling tasks, in which it doesn't belong. See my P.S. in my previous post. If weird rules just affect stuff inside a theoretical system - fine. If those rules result in massive logical breaks when making explanations about reality, not fine.Coldie said:
No, no no no. The problem with that proof is the whole infinity thing. Infinity is just a concept. Basically, 10x0.999.. should equal 9.999..8havass said:
Because infinity is supposed to be, well, forever, the 8 is kinda ignored in that proof, but it should be on the end of that never ending number. You see why it's a problem?
OT: I think my stance on this is rather obvious. 0.9 recurring doesn't equal 1. It is in fact, 1x10^(-infinity) less.
How many infinities (including mathematical points) can you spot in physics? Why is it that the maths which use those do work, and yet, the infinities themselves have never been observed directly? Here's a hint: perhaps the most reasonable use of a mathematical point, for calculating reality, is like a "position-marker" (while never actually using it infinitely precise... its just there in the models, and then in practice gets enough precision as necessary).Lukeje said:
P.S.: I could go into more detail, about how numbers and the ranges in-between, are directly derived from how we "address" things in our perception - and thus, actually come from something very intuitive and imaginative... and how this mechanic resulted in a lot of misunderstandings.... including the wave/particle dualism... but this would derail the thread too much.
Which is equivalent to zero. Which means there is no difference. Which means .999... = 1brunothepig said:
I have a similar proof to the one with 0.9999... = 1
See if you can find the mistake and you have the same mistake for the other one...
1-1 = 0
(1-1)+(1-1)+(1-1)+(1-1)+(1-1)+(1-1)+(1-1)+(1-1) = 0
(1-1)+(1-1)+(1-1)+(1-1)+(1-1)+(1-1)+(1-1)+(1-1)+(1-1)+(1-1)+(1-1)+(1-1)+..... = 0
1+(-1+1)+(-1+1)+(-1+1)+(-1+1)+(-1+1)+(-1+1)+(-1+1)+(-1+1)+(-1+1)+(-1+1)+..... = 0
1 = 0
See...perfectly correct and logical...
See if you can find the mistake and you have the same mistake for the other one...
1-1 = 0
(1-1)+(1-1)+(1-1)+(1-1)+(1-1)+(1-1)+(1-1)+(1-1) = 0
(1-1)+(1-1)+(1-1)+(1-1)+(1-1)+(1-1)+(1-1)+(1-1)+(1-1)+(1-1)+(1-1)+(1-1)+..... = 0
1+(-1+1)+(-1+1)+(-1+1)+(-1+1)+(-1+1)+(-1+1)+(-1+1)+(-1+1)+(-1+1)+(-1+1)+..... = 0
1 = 0
See...perfectly correct and logical...
The mistake is how people deal with infinity. One cannot write an infinite number of ciphers, so we stop at a certain point and just hint at infinity (by using '...' for example). But if you want to do real math with infinite numbers, you cannot just hint at infinity, you must take it into account completely.
So to proof that 0.99999 =/= 1 we write 0.999999...99 instead (the last two ciphers symbolize the theoretical 'end' of the infinite number)
x = 0.999999...99
10x = 9.999999...90
10x-x = 9.99999...90 - 0.999999...99
9x = 8.9999999...91
x = 0.999999...99
Here you go.
In my example there is a -1 still waiting at the end of infinity that I omitted.
So to proof that 0.99999 =/= 1 we write 0.999999...99 instead (the last two ciphers symbolize the theoretical 'end' of the infinite number)
x = 0.999999...99
10x = 9.999999...90
10x-x = 9.99999...90 - 0.999999...99
9x = 8.9999999...91
x = 0.999999...99
Here you go.
In my example there is a -1 still waiting at the end of infinity that I omitted.
No it's not, but the difference between 0.9*[footnote]the * represents recurring.[/footnote] and 1 is 0.0*1 and since there are infinite 0's then the difference is infinitely small.
Anyone with a basic understanding of maths can tell the difference between equal to and infinitely close to.
Also, this topic is used too much.
On a side note, the last thread I saw of this had the most stupid post I saw in a long time. It went something like a=1 b=0.9* and abc=2 therefore ab=2 and b=1.
Anyone with a basic understanding of maths can tell the difference between equal to and infinitely close to.
Also, this topic is used too much.
On a side note, the last thread I saw of this had the most stupid post I saw in a long time. It went something like a=1 b=0.9* and abc=2 therefore ab=2 and b=1.
I didn't say that all of math was intuitive, I said that all of mathematics finds its base in intuition. Axioms, by definition, exist either to codify intuitions (intuitions that we find basic and inescapable) or to solve paradoxes that arise when those intuitions collide. The sort of austerity you describe is an illusion created by the latter type of axiom: the sort that are required to maintain consistency within the system described. The problem is that when we take our basic intuitions and attempt to form more complex naive theories by extrapolating from them without extreme care, we introduce errors into our computation. Mathematics is, in essence, a way to perform careful extrapolation from our basic intuitions. It's ludicrous to claim any alternative. If mathematics doesn't stem from intuitions, where does it come from? You end up some sort of bizarre Platonist. Intuitions are all you've got. If you're actually interested in these questions, you should look into the philosophical foundations of mathematics and philosophy of science in general. There's some good discussion in the developmental psychology literature regarding acquisition of number theory as well.Coldie said:
People who know mathematics do not necessarily know the underpinnings of mathematics and it's statements like this, talking about how mathematics is somehow disjoint from reality and intuition, that lead the general public to reject complex mathematical results.
RE the actual question: If you don't think .999...=1, you probably think that it's less than 1. If it's less than one, you need to add something to it to make it one. What are you going to add? .000... with a 1 and the end? If there are an infinity of zeroes, WHAT END?
The issue of infinity as a number not being useful in the real world is also blatantly false. Many of these issues are extraordinarily important in physics and engineering. See therodynamics, hydrodynamics, and electrical engineering in particular (specifically regarding complex analysis).
This is a question of limits for asymtotes, and the function used to obtain these values is called lim.
So for this case is
lim(x)=1 for x -> 1
It's used in the proof of integrations and differentials. Where you slice the lines infinately thin and then add up.
So for this case is
lim(x)=1 for x -> 1
It's used in the proof of integrations and differentials. Where you slice the lines infinately thin and then add up.
I think anything that tries to grasp at infinity is flawed. Even if just on the grounds that one can't possibly understand what it doesn't know.
No one knows what happens once you count to infinity. Because as living creatures we cannot. I assume the clouds open up, God rides a flaming unicorn to the front of your house/apartment, and proceeds to teach you how to actually beat The Sims.
PS: No your Sims dying without children doesn't constitute *beating* the game. Duh.
No one knows what happens once you count to infinity. Because as living creatures we cannot. I assume the clouds open up, God rides a flaming unicorn to the front of your house/apartment, and proceeds to teach you how to actually beat The Sims.
PS: No your Sims dying without children doesn't constitute *beating* the game. Duh.
I really don't want to read all post and people might have said this, butRawle Lucas said:
9.999... = 9 + x =/= 10x - x = 9x = 8.99999999...
But if you don't want to be exact, you can always say that 0.99999 is 1. But there is no equal sign in there. Two different numbers are not equal.
And this is why we have different number sets like rational, irrational and real numbersepninja said:
Maybe I'm not being scientific enough but, isn't the answer that it's close enough that no-one should really care if it is or not?
If I had to choose between a million bucks and 0.99999... of a million bucks, I wouldn't waste a lot of time thinking about it. (it'd be the million because the other option might be a trap.)
If I had to choose between a million bucks and 0.99999... of a million bucks, I wouldn't waste a lot of time thinking about it. (it'd be the million because the other option might be a trap.)
Doesn't matter how much algebra you do, 0.999999999 of anything is less than a complete one. Therefore, they are not the same.
Why is everyone seeming to argue that this infinity needs to be calculated in real time?Klopy said:Some of the math in this thread is flawed... jeez. Double check, please.
.9999... is not equal to 1.
Why?
Still being in high school, and with my chemistry background, I would have to say that .9 etc. is not equal to 1 because of its significant figures. You can round up when the math is over, but it will never be correct. .9999999 will always be <1, no matter how close it gets. In the math world, this is just how it has to be.
In real life, it would get so close to 1 that it wouldn't really matter.
But in theoretical conversations, it will always be <1.
By which I mean, people are saying "Sure, you can keep adding those 9s, but you'll never actually reach forever."
It doesn't reach forever, true. It just is.
It is infinite, right now. It won't "never reach forever", it is forever already.
That's what infinite means.
I...I don't get what's difficult about that.
Still, not a Math Major here, maybe infinity is treated differently in maths. I'd find it difficult to calculate with an infinity that actually equalled an ever-fluctuating rational number though, myself.