Poll: Does 0.99 Recurring = 1
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Soldato
No. Pi is pi.
See proofs posted earlier.
As I said, you are trying to link it to "common experience", which makes it confusing. Maths does that, its not always the same as common sense.
If an inconcistency exists, then someone is welcome to post it. True, you cannot say that it doesn't it. If those who say 0.9r isn't 1, then the inconcistency is in there somewhere, and even with GCSE (and certainly A Level) maths, you should be able to show 1>1
Fire away......Well we don't all know better than God himself now do we
Caporegime
so by that definition, 0.99r = to 0.99r ? Or is there are different representation of the number 0.99r ?
After reading what everyone has to say(Well i read the first 20ish pages) i have come up with a comprehensive answer (theory). Please bear with me im not the best at explaining these things.
My theory is that 0.9r is the equivalent of 1, but does not = 1.
now correct me if im wrong but
1-1 = 0
and
0.9r-1 = 0 (as seen by maths)
but common sence suggests that 0.9r < 1 so how can the answer be 0.
well (in my world) it isnt. The real answer has to be,
0.9r-1 = (0.1 * 10^- infinity).
but since infinity is.....well..... infinite the 1 cannot be added and is therefore ignored in maths making the answer 0.
But in the real world the difference still exists making the 0.9 the equivalent of 1 but not = 1.
My theory is that 0.9r is the equivalent of 1, but does not = 1.
now correct me if im wrong but
1-1 = 0
and
0.9r-1 = 0 (as seen by maths)
but common sence suggests that 0.9r < 1 so how can the answer be 0.
well (in my world) it isnt. The real answer has to be,
0.9r-1 = (0.1 * 10^- infinity).
but since infinity is.....well..... infinite the 1 cannot be added and is therefore ignored in maths making the answer 0.
But in the real world the difference still exists making the 0.9 the equivalent of 1 but not = 1.
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Soldato
Common sense says 0.9r<1, logical argument (which is maths, but using longer words) says 0.9r = 1.
Associate
Erm...
anyway... He doesnt think it does, but then again, what does he know Godel's question is an interesting one. One of the things his theory says is that in any formal system, there are unprovable truths. This, could be one of them. However, seeing as a formal system is based on "given" theorums (axioms) and "rules" (addition, subtraction, etc.)., the only time you're going to get something where you don't know is true is through self-reference.
Basically, multiplication can never be wrong, as it's one of the rules of the system itself.
And as I said before, 0.999r is just another one of the infinite representations of the concept commonly referred to as "1". Just like 9-8. Or e^(i.pi) +2. There's no reason why it exists, it just does.
As Grrr said, 0.9r is not another one of those numbers you can just write on a piece of paper. If you wrote a million 9's per second until the end of time you wouldn't finish writing it. People don't seem to get that. THere's no conept of adding another 9 on the end because there *is* no end.
/bangs head on table.
Basically, multiplication can never be wrong, as it's one of the rules of the system itself.
And as I said before, 0.999r is just another one of the infinite representations of the concept commonly referred to as "1". Just like 9-8. Or e^(i.pi) +2. There's no reason why it exists, it just does.
As Grrr said, 0.9r is not another one of those numbers you can just write on a piece of paper. If you wrote a million 9's per second until the end of time you wouldn't finish writing it. People don't seem to get that. THere's no conept of adding another 9 on the end because there *is* no end.
/bangs head on table.
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Soldato
Not a lot compared to Gauss and Euler.Originally posted by hendrix
Given the nature the thread, its important.
Soldato
I think you'll find it difficult to point out anywhere where I dismissed philosophy as anything, because I didn't. My point was merely that people here seem to be reading the thread title, thinking to themselves "hmm, they look different, so they must be different" and then posting as such without reading anything in the thread - ignoring the fact that their issues have been addressed several times already.
I do think you misinterpreted my comment. I put "philosophical" inside quotation marks simply in order to differentiate it from the "mathematical" arguments, not so as to disparage the philosophical way of seeing things in any way.
In fact, as you'll see, I said "where, unlike in Maths, there are valid opposing opinions and there can be debate". This was a response to people saying that, in effect, no matter how many proofs are put forward, they will not acknowledge that "mathematically" 0.9r=1. And what I point out is that proofs are proofs. If they're demonstrated flawed, they cannot be "argued" for as such. If they're correct, you can't simply refuse to accept them - by their very definition, there is no philosophical debate about mathematical proofs.
I think you'll find that I (by which I mean myself personally, I can't speak for others) have been speaking in a strictly mathematical sense. Several times I have emphasised that "mathematically", 0.9r=1. And this obviously refers to our current system of math, I'm not about to debate what we get to in fifty years time when we may have grasped the concept of infinity.
Now, I'm not saying that philosophy has no place in this debate - quite the contrary in fact, it is, by its very definition an important part of it - however, it is not one I am prepared to debate at this point in time, which is why I restricted my comments to this thread; this thread seems the more mathematical of the two, the other seems more philosophical. If I were to get involved in the other as well, I would have no time to do anything else!
Soldato
Thats not a proof, thats a poorly constructed argument, which is flawed
See, this is why I hate maths at such complex levels... they seem to create all these lame theorys that currently defeat simple laws of logic. Currently infinity only exists within numbers, right?
Infinity does not exist physically. Logically 0.9r ... infiniate amount of 9's and it's still not quite 1! 1 is a whole number so how does a decimal = 1?
Infinity does not exist physically. Logically 0.9r ... infiniate amount of 9's and it's still not quite 1! 1 is a whole number so how does a decimal = 1?
I know thats why i changed it, but you didnt comment on my theory.
how can 0.9r - 1= 0 without first equating 0.9r to = 1? And if the answer is not 0 the two are not equal.
hence as i said i see 0.9r as the equivalent of 1 not = 1
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