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#2 Exercises » . » 2007-02-25 11:09:19
- kylekatarn
- Replies: 3
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#6 Jokes » . » 2007-02-13 07:47:35
- kylekatarn
- Replies: 9
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#7 Re: This is Cool » 0.9999....(recurring) = 1? » 2007-02-12 08:13:22
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INFINITE 0.9 <> 1 PROOF : FORMULA : By,Anthony.R.Brown,12/02/07
----------------------------------------------------------------------------------------------------------------A = 1 " Single Start Value For 1 "
B = 0.9 " Single Start Value For 0.9 "
C ( A/B ) x B " Infinite 0.9 Value "
D ( A - C ) " Infinite < 1 Value "
C <> ( C + D ) " INFINITE 0.9 <> 1 "
----------------------------------------------------------------------------------------------------------------
OK, but be happy! 
0.(9) equals 1... and the world doesn't end if you refuse it.
#8 Exercises » . » 2007-02-10 05:15:02
- kylekatarn
- Replies: 0
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#9 Maths Is Fun - Suggestions and Comments » . » 2007-02-10 04:18:17
- kylekatarn
- Replies: 7
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#10 Re: This is Cool » 0.9999....(recurring) = 1? » 2007-02-10 02:02:27
There is no "last 9". That's why we use limits to understand what really means 0.(9).
I bet you didn't look to the definition of limit yet. : (
#11 Re: This is Cool » INFINITE 0.9 <> 1 PROOF By,Anthony.R.Brown,15/01/07. » 2007-02-10 02:00:26
http://www.mathsisfun.com/forum/viewtop … 965#p58966
*note*.Since we are discussing the same thing on two threads "0.9999 (recurring)= 1" and " INFINITE 0.9<>1 PROOF" why not to lock one thread and continue on the other?
#12 Re: This is Cool » 0.9999....(recurring) = 1? » 2007-02-10 01:47:03
Of course there is always another 9 (-__-)' it's obvious. That's not the question.
IS 0.(9) = 1 ? YES.
And your analysis of finite decimals:
0.9.....9
`---´
n ∈ N¹
...will never show that 0.(9) ≠ 1. Shows precisely the opposite.
if you consider the sequence s[k] : {0.9, 0.99, 0.999, 0.9999, ... }
for all Δ>0 exists an 'N' such that |s[k] - 1| < Δ whenever k>N.
Therefore
And now try to guess what 0.(9) means? 1.
This is the question in this thread, answered thousands of times, thousands of different ways. Everyone knows 0.9 < 1, 0.99 < 1, etc. But not everyone seems to understand why 0.(9) = 1. And someone keeps refusing the concepts of limit and infinite series.
#13 Re: This is Cool » INFINITE 0.9 <> 1 PROOF By,Anthony.R.Brown,15/01/07. » 2007-02-09 08:48:05
1 - 0.9 = 0.1 " Notice this is a number! with a 1 on the end " " If it's not? then funny if you add " 0.1 to 0.9 you get 1
1 - 0.99 = 0.01 " Notice this is a number! with a 1 on the end " " If it's not? then funny! if you add " 0.01 to 0.99 you get 1
1 - 0.999 = 0.001 " Notice this is a number! with a 1 on the end " " If it's not? then funny! if you add " 0.001 to 0.999 you get 1
The Above is Only a Small sample from the Start Onwards! But I can Assure you! is Infinitely possible!
Because 1 - ( Another Number < 1 ) Will always have an Infinite Difference!!!
P.s the 1 "at the End!" and the 9 "at the End!" is a term to decribe! at the End of an Infinite Sequence! for as far as we have Calculated! and can see on paper!
We all know it's not an actual End!! but in the Above three examples,we can see them at the End Three Times!!
Why do you keep capitalizing the first letter of some words? Are you trying to sound "Biblical" or something?:/
*NOTE*: You still haven't shown that 0.(9) ≠ 1 using valid arguments/proof.
#14 Re: This is Cool » INFINITE 0.9 <> 1 PROOF By,Anthony.R.Brown,15/01/07. » 2007-02-08 01:52:52
Anthony.R.Brown wrote:Don't worry we all detect your Humorous Nervousness! it's always a sign when confronting the Truth!
Don't worry, we all detect your desperation! It is evident in the fact that you avoid the points you don't want to talk about, don't answer questions which would otherwise prove you wrong, and keep starting new threads in the vain hope that saying it over and over again will either make it true, or just make us believe.
And all because you're not big enough to admit when you're wrong.
Again, yet another question that I asked in a post above:
I ask you, what is the number that you have to add when the 9's go on without end?
Please answer it, bearing in mind that 0.0000...0001 is not an actual number.
I bet he will say something like "N4 - V564 < XZ<L^OL = 1.000000000000000...01 therefore V2-G^p < 1 !!!!! AHHH!! 0.99999.. = B +1 so Yes, The Truth!
#15 Re: This is Cool » IF TWO NUMBERS START WITH A DIFFERENCE IN THEIR VALUES! By A.R.B » 2007-02-08 01:33:12
Anthony, you "theorem" just got pwnd by the Trivial case:P
#16 Re: This is Cool » INFINITE 0.9 <> 1 PROOF By,Anthony.R.Brown,15/01/07. » 2007-02-08 00:53:44
http://en.wikipedia.org/wiki/0.999...
* pay close attention to the topics
"Real analysis"
"Skepticism in education"
"In popular culture"
http://en.wikipedia.org/wiki/Recurring_decimal
* pay close attention to the topics
"Notation"
"Why all repeating or terminating decimals must be rational numbers"
If Wikipedia still does not convince you, I suggest you try Wolfram Science and search on this topics. The site is run by people who really know about Maths.
After these readings I doubt anyone can believe such nonsense as 0.(9) ≠ 1. One thing is not knowing some more advanced stuff like series and limits, that's OK, we all learn that sooner or later. Another one is denying what the entire world is telling us.
Believe me, one day you will find 0.(9) = 1 so natural as 1 = 1
#17 Re: This is Cool » INFINITE 0.9 <> 1 PROOF By,Anthony.R.Brown,15/01/07. » 2007-02-07 03:16:57
no..no... the funniest part is :
( 0.1 ) = 1
( 0.01 ) = 1
( 0.001 ) = 1
( 0.0001 ) = 1
( 0.00001 ) = 1
( 0.000001 ) = 1
( 0.0000001 ) = 1
( 0.00000001 ) = 1
( 0.000000001 ) = 1
( 0.0000000001 ) = 1
I guess Anthony's "curved-bra-ket" operators are very powerfull. Something like this:
( . ) : R ----> {1}
x ----> 1
#18 Re: This is Cool » 0.9999....(recurring) = 1? » 2007-02-07 02:06:19
when you write down 0.999..., you may be asked to define what you really mean by that. Note that:
So, what we really mean when we write down 0.999... is:
Which, if we were to be fully rigorous, means that:
So the above is what we really mean by 0.999... - so the question is, is the above expression equal to one? Well... yes, it is.
There isn't much more to say on this subject, the proof is there, the symbols, notations, the meanings. If you, Anthony and others don't accept 0.(9) = 1, that's fine to me. You are free to reinvent algebra and calculus if you want to, but I prefer to stick with concepts that have been developed through centuries of mathematical research.
#19 Re: This is Cool » 0.9999....(recurring) = 1? » 2007-02-07 00:02:08
kylekatarn wrote:The day you have lectures on Limits and Infinite Series, come here again and you will make a little smile when re-reading your theories
Are you suggesting that Ricky doesn't know limits and infinite series? (Around post 60 he admitted "we simply defined it in limits")
It wasn't a suggestion. Someone who doesn't ""believe"" 0.(9) = 1 it's because one of two things:
- he/she doesn't really know that 0.(9) is formed by the infinite sum 0.9 + 0.09 + 0.009 + ... = 1
- he/she may know limits and infinite series but he/she is trying to show something completely out of Mathematics. 0.(9) equals 1, whether one likes it or not.
All it took me to understand and accept the equality of 0.(9) and 1 was notion of limit and infinite sum. Understand, not just "knowing about". If someone really understands but keep saying "0.(9) ≠ 1 because of this", "0.(9) ≠ 1 because of that", "0.(9) ≠ 1 because of the infinite difference Z ou W" then something is wrong.
#20 Re: This is Cool » 0.9999....(recurring) = 1? » 2007-02-06 04:00:46
The day you have lectures on Limits and Infinite Series, come here again and you will make a little smile when re-reading your theories
#21 Re: This is Cool » INFINITE 0.9 <> 1 PROOF By,Anthony.R.Brown,15/01/07. » 2007-02-06 03:44:39
Come on, Anthony isn't yet a Believer. It's our job to convert him to the "0.(9) = 0" Revelation:)
lol;)
#22 Re: This is Cool » INFINITE 0.9 <> 1 PROOF By,Anthony.R.Brown,15/01/07. » 2007-02-06 03:04:03
Anthony.R.Brown wrote:INFINITE 0.9 <> 1 PROOF : CONCLUSION By,Anthony.R.Brown,06/02/07.
----------------------------------------------------------------------------------------------------------------After all the Thoughts! and Arguments! the Solution is really Quite Simple!
V1 = 0.9999999999...." = The 0.9 Value from the Start Onwards! "
V2 = 0.0000000001...." = The < 1 Value from the Start Onwards! "
(a) The Above will always be True! as Calculated in the Equation Below
( V1 + V2 ) = 1
(b) There will always be Two Values from the Start Onwards
(c) Neither of the Individual Values will ever Equal 1
(d) There will always be an Infinite Difference ( V1 <> V2 )
OH! MY! GOD! I see it now! How, oh how could I have been - could we all have been - so UTTERLY stoopid to consider ourselves correct in the face of such blatantly falacious "reasoning" (or so we called it!).
Anthony - I am truly sorry, I owe you the largest debt of gratitude for opening my eyes. Not just to the world... but to the truth.
LOL, this is getting funnier indeed^^;P
#23 Re: This is Cool » INFINITE 0.9 <> 1 PROOF By,Anthony.R.Brown,15/01/07. » 2007-02-05 02:58:11
INFINITE 0.9 <> 1 PROOF : CONCLUSION By,Anthony.R.Brown,06/02/07.
----------------------------------------------------------------------------------------------------------------After all the Thoughts! and Arguments! the Solution is really Quite Simple!
V1 = 0.9999999999...." = The 0.9 Value from the Start Onwards! "
V2 = 0.0000000001...." = The < 1 Value from the Start Onwards! "
(a) The Above will always be True! as Calculated in the Equation Below
( V1 + V2 ) = 1
(b) There will always be Two Values from the Start Onwards
(c) Neither of the Individual Values will ever Equal 1
(d) There will always be an Infinite Difference ( V1 <> V2 )
assuming you are using '...' to indicate that last digit repeats forever, let's review you calculations, hoping not to miss any digits:
V1 = 0.(9)
V2 = 0.000000000(1) = (1/9)*10^(-9)
V1 + V2 = 1
therefore:
V1 = 1 - V2
V1 = 1 - (1/9)*10^(-9)
V1 = 0.999999999(8)
This means you believe that:
0.(9) = 0.999999999(8)
and since LHS has infinite digits qe can rewrite it as:
0.999999999(9) = 0.999999999(8)
nope, I still can't agree with you.