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RE: [split] 0.999... equals 1
October 16, 2009 at 10:57 am
(October 16, 2009 at 9:12 am)leo-rcc Wrote: 0.3r is not 1/3, it is an approximation as close to 1/3 you can get in decimals. 0.1r is not 1/9 in decimals but an approximation. This is not true. Anyone with a paper and pencil and see that 1 divided by three generates 3's without end. There is no limitation being placed upon the actions, and we can say that the 3's repeat endlessly. Saying .3r is how we represent this and it is an exact value.
Also, the decimal system is not at fault here. I can do the same proof in any number system and still have to rely on infinitely repeating numbers.
In base3,
Code: x = 0.2r
10x = 2.2r
10x - x = 2.2r - .2r
2x = 2
x = 1
0.2r = 1
If your beef is with infinitely repeating numbers, and you don't accept long division as proof of their accuracy, we are indeed at an impassé.
I think SaeRules is also of this stance?
- Meatball
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RE: [split] 0.999... equals 1
October 16, 2009 at 12:39 pm
(October 16, 2009 at 9:38 am)EvidenceVsFaith Wrote:
You completely miss the point - but you also seem to blindly accept - so really there's no point talking with you. Same with everyone - you're so sure you're right you've given up thinking. As Leo says.. you're spouting theistic crap!
At every point along the infinite series, there is a tenth shortfall, infinitely. Maybe it can be written 10-0.1r
(October 16, 2009 at 9:38 am)EvidenceVsFaith Wrote: Quote:Fact remains.. the 2 can never converge, no matter that you can't name the infinitesimal, we know it's there at every stage. There is no end to infinite.. so the infinitesimal amount has no end either. Just because I can't name the number doesn't mean it doesn't exist. We KNOW it HAS to exist using logic. the logical proofs deny this, which is their error.
No, we knot that it logically can't exist. Because - using logic - there can be no number between 0.9r and 1 because there is no gap between them because the 9s on the end go on for infinity. It's not a matter that you can't name it, it's a matter of the fact that it logically can't exist - not that it logically has to! It can't!
The logical proofs deny what? Deny the fact that according to you there can be a number between 0.9r and 1 when there logically can't because there can be no number between them?
We knot???
How can there be no gap if there's a tenth gap to infinity - you talk shite!
(October 16, 2009 at 9:38 am)EvidenceVsFaith Wrote: fr0d0 Wrote:Say you had an infinite railway line. You know the line moves closer to the border 9/10ths every mile. On your (incredibly short but long haha!  ...this would have to be an incredibly shrinking train and track! LOL) train journey, at every mile you notice the gap decreasing by 9/10ths... but it NEVER reaches 10/10ths at any point.
we're not talking about anything 'reaching' anything. 0.9r doesn't have to reach 1, it's a matter that it logically must be the same number represented in decimal: Because there can't logically be a number between it and 1 because the 9s on the end of 0.9r go on for infinity!
What utter tosh Evie! You are the master of misunderstanding. I NEVER SAID I REACHED FUCKING INFINITY! Show me where I did!?!
Read the fucking words and come back to me if you have a fucking point - stop wasting my time with your fucking misobservations all the time!!!
(October 16, 2009 at 9:38 am)EvidenceVsFaith Wrote: Quote: It cannot, because we've already established that it keeps to 9/10ths to infinity, the law says so.. "no train track shall ever touch the damn border!!!" (damn politicians!!)
Infinity is not a number so you can't have 9/10s of it, that's a different matter. We are not talking about infinity itself, but an infinite number of 9s recurring on the end of 0.9.
I'm not talking about infinity as a whole, but the journey to infinity, which we can see by the progression of 9's, follows a pattern of 9/10ths of the whole... infinitely.
As we know the pattern MUST stay at 9, we can know that it will never converge
I thought my analogy was a good one, and I'd like to see a sensible explanation of why it isn't correct.
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RE: [split] 0.999... equals 1
October 16, 2009 at 3:42 pm
This is mainly for anyone still interested in the proofs, since this website sums them up quite nicely.
http://www.purplemath.com/modules/howcan1.htm
There are a few there that I haven't mentioned, and are from other branches of mathematics. It also has an infinite series proof which is pretty cool.
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RE: [split] 0.999... equals 1
October 16, 2009 at 5:16 pm
It is a very cool topic IMO.
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RE: [split] 0.999... equals 1
October 18, 2009 at 10:45 pm
i disagree with the statement 0.9repeating = 1, because, not matter how infinitely close it is to 1, it never can be.
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RE: [split] 0.999... equals 1
October 19, 2009 at 12:36 am
(October 18, 2009 at 10:45 pm)Armitando Wrote: i disagree with the statement 0.9repeating = 1, because, not matter how infinitely close it is to 1, it never can be.
0.9... is infinitely long.
It is not infinitely large, the limit is 1.
The limit of a series, even an infinite series, must be part of the series.
If 1 is the limit of 0.9... then 1 must be part of the series 0.9... and thus equal to 1.
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RE: [split] 0.999... equals 1
October 19, 2009 at 12:53 am
(This post was last modified: October 19, 2009 at 12:53 am by theblindferrengi.)
But 0.999... is not a series, it is a value, and since the distance between it and 1 is infinitely small (1/infinity, aka 0 because a distance that is infinitely small would be shorter than the planck length) it is equal to 1.
Has anyone really been far even as decided to use even go want to do look more like?
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RE: [split] 0.999... equals 1
October 19, 2009 at 4:11 am
0.999... can be reduced to the following infinitely long series:
0.9 + 0.09 + 0.009 + 0.0009 ...
This can be further reduced to:
0.9 + (0.9 * 0.1) + (0.9 * 0.1 * 0.1) + (0.9 * 0.1 * 0.1 * 0.1) ...
This series follows the general pattern of infinite series, and so we can use the infinite sum formula to work out the total:
Total = a / (1 - r)
a being 0.9
r being 0.1
So, the sum of the infinite series obtained from breaking down 0.999... is:
0.999... = 0.9 / 1 - 0.1
0.999... = 0.9 / 0.9
0.999... = 1
Q. E. fuckin' D. bitches. (again)
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RE: [split] 0.999... equals 1
October 19, 2009 at 8:15 am
The truth of the matter is that both answers are correct. 0.9... = 1 and 0.9... is never 1
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RE: [split] 0.999... equals 1
October 19, 2009 at 8:19 am
They can't both be true, it's a contradiction - Nice to see how flawed your logic is.
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