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.9 repeating = 1? Is our numerical system flawed?

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posted on Apr, 9 2005 @ 03:35 AM
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PI: January 4, 2002


This is my first paper. It is only to help me prepare for school. The content is unimportant, but the style and page layout is important. I want this paper to be double spaced with a font size of twelve. The borders are to be at least ¾ of an inch on all sides. The grammar, punctuation, and spelling are also very important. I will now type a decimal notation approximation of pi to as many decimal places as I can from memory. I have not practiced recalling pi for at least three weeks now, so this may not be correct.
An attempt at recalling pi to the two hundred fiftieth decimal place: 3.141592653589793238462643383279502884197169399375105820974944592*64062862089986280348253421170679821480865132823066470938446095505822317253594081 284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091

Well, that was my best shot. I will now check my number with the one in my original source book, The Joy Of Pi. I feel pretty good about my answer.
All right. My number is correct! The only problem is that I thought that I had memorized it to 250 decimal places and I just counted it and came up with 248 decimal places. I must recount. Well, on second count I get 251. Is that not precious? I can memorize a number that is that long but then I cannot count that high! Finally, I count 250 decimal places. I think that is accurate enough for me.
Actually, 355/113 is accurate enough for almost anything in the real world. That fraction is accurate to six decimal places, or one millionth.

bg13




posted on Apr, 11 2005 @ 03:23 PM
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1/9 does not equal .111111..... It equals 1/9. You cannot convert that number into an even. I ould quote someone who stated this earlier but I haven't been able to figure that out yet. He said something about how you always step halfway to the wall and so on, yuou know how it goes. that theroy sort of applies here. you will always have a fraction left over from your division. please explain the geometric system in your way because it just isn't working for me


[edit on 11-4-2005 by Maggot Minion]



posted on Apr, 11 2005 @ 04:11 PM
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Originally posted by Maggot Minion
1/9 does not equal .111111..... It equals 1/9. You cannot convert that number into an even. I ould quote someone who stated this earlier but I haven't been able to figure that out yet. He said something about how you always step halfway to the wall and so on, yuou know how it goes. that theroy sort of applies here. you will always have a fraction left over from your division. please explain the geometric system in your way because it just isn't working for me


[edit on 11-4-2005 by Maggot Minion]


Once again, and hopefully for all, this is ONLY a question of base. Depending on the base you're writing numbers in, 1/3 or 1/9 can be totally and completely finite, or totally and completely infinite. However, pi is irrational and transcendent (sp?). This means that (at least in our decimal system, but greatly suspected to be in any base) pi is to be written to the infinite... It never ends...



posted on Apr, 11 2005 @ 04:34 PM
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the implication is that mathematical rigor is an illusion and math is nothing more than a highly structured system of intuitive insight.

how many of you know the bizarre phenomenon which presents itself in solving calculus problems? most of the answers I get are intuitively arrived at regardless of tables or methodology used. The symbolism of math and all of its axioms, rules, definitions, theorems, corollaries etc., simply seem to be a crowd of cheering spectators compelling me to go in a certain direction.

interestingly, the history of math shows that many of math's most difficult problems have been resolved through meditations, dreams, and in some cases visions. Many numbers were used in the occult, and many considered magical.

could math have a spiritual root? could numbers be merely mental hooks in spiritual pigeon holes, and the more defined or exact the number is, the more potent the force of that number?

numbers are spirit?

ê¿ê

[edit on 11-4-2005 by sozzledboot]



posted on Apr, 11 2005 @ 06:10 PM
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many of math's most difficult problems...


They're only the most famous ones, there are vast numbers of mathematical problems that have to be worked out manually, just look up Euler and you'll see that while he was probably the most prolific and gifted mathematician ever born he also did some serious donkey work in his studies. The most 'beautiful' theorems are the simple, elegant ones that don't require brute force to solve or prove but these solution were only ever derived at after many hours of work. I can't remember who said it but I think it describes the way mathematical proofs are presented perfectly, it goes along the lines of ' a mathematician is like a fox walking through snow, you know where he started and you know where he ended but along the way he was wiping his tracks out with his tail and its up to you to see how he got to where he ended up'.

As for maths being some sort of spiritual thing....


Calvin: You know, I don't think math is a science, I think it's a religion.
Hobbes: A religion?
Calvin: Yeah. All these equations are like miracles. You take two numbers and when you add them, they magically become one NEW number ! No one can say how it happens. You either believe it or you don't. [Pointing at his math book] This whole book is full of things that have to be accepted on faith ! It's a religion !
Hobbes: And in the public schools no less. Call a lawyer.
Calvin: [Looking at his homework] As a math atheist, I should be excused from this.


Mathematics is a closed logical system, it has fundamental axioms (unprovable, self-evident truths, thats probably the spiritual bit) from which eveything else can be (or at least should be) derived. Secondary (High) school maths is not like this, things are given to you, half-hearted proofs are attempted (they are correct but you are never really told why), and you are told to accept them (unless you had a good teacher, like i think i had
).



you will always have a fraction left over from your division

but you won't because .111~ goes on forever, ad infinitum, por siempre, pour toujours, für immer, per sempre, para sempre, навсегда, this translation button is opera is addictive....
but i hope you get the idea, the .111~ thing never ends there is no missing bit at the end because there is no end.

[edit on 11/4/05 by cmdrpaddy]



posted on Apr, 12 2005 @ 12:04 AM
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Vagabond, Blizzard Entertainment was actually the first to discover this formula, I believe. It was part of an April Fools joke.

You can view the discovery here (exact formula as you've described in your first post):

www.blizzard.com...



posted on Apr, 12 2005 @ 01:22 AM
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.
If you think about it all integers end in a string of repeating zeros.
1.0000000000000000....

if you are worried that something unpredictable is going to happen somewhere vauge out there near the infinite place for 0.9999999....

Why don't you worry the same thing for 1.000000000.... ?

There is infact no difference in either situation.

All rational numbers end in repeating sequences of digits.
.



posted on Apr, 13 2005 @ 03:05 AM
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The best way to look at .9 repeating is as the sum from n = 1 to infinity of one over ten to the nth power. The definition of a limit at infinity (from An Introduction to Analysis 2nd ed by William R. Wade) is | f (x) - L | < e for any e > 0. Pick any number greater than zero, no matter how small, and it will still be greater than the absolute value of .9 repeating minus 1. Therefore the limit of the sum .9 repeating represents is 1, and this is the next best thing to saying .9 repeating equals 1.



posted on Apr, 13 2005 @ 03:44 AM
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Brain Fart, I meant .9 repeating is the sum of 9 TIMES ( 1 / 10 ^ n) for n = 1 to infinity, but went on to describe .1 repeating. Don't drink and derive!



posted on Apr, 17 2005 @ 05:30 PM
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.
In a sense it is like seeing all the parts of one.
Like a parts list.
on one side you have a whole assembled car on the other your have an ordered stack of all the car parts needed to assemble that car.

Sort of like the human genome project. We have a huge parts list about which we barely have a clue how they go together to make things work or make other things happen.

In many respects 0.9999.. is equivalent to 1 but conceptually they are not the same.

0.9999... is the infinitely exploded view/diagram of 1.
Sort of a perpindicular perspective of 1.

1 is road ready, 0.99999... needs assembly.

'parts is parts'

It is the fractal of one.
partial dimensionality function of a whole dimension.
recursive fractal extraction or combination of portions of one.

anatomy of one.

Maybe this is it.
They are the same quantity, but they are not the same number

A number is a symbolic repesentation isn't it?

same hand with a different glove on.
.

[edit on 17-4-2005 by slank]



posted on Apr, 17 2005 @ 07:21 PM
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The equation that was first posted: X=.999
10X= 9.999
10-X = 9X
9X = 9
1X = 1
1= .999

That equation is completly wrong.

If X = .999 then 10 multiplies by X = 9.99 not 9.999.
10x - x does = 9x but where did you get 9x =9??!!!
9x would be equal to 8.991
Therefore X = .999

You've obviously made a mistake, you can check this on a normal calculator.


[edit on 17-4-2005 by PeteTPP]



posted on Apr, 19 2005 @ 01:22 AM
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Originally posted by PeteTPP
The equation that was first posted: X=.999
10X= 9.999
10-X = 9X
9X = 9
1X = 1
1= .999
That equation is completly wrong.
If X = .999 then 10 multiplies by X = 9.99 not 9.999.
10x - x does = 9x but where did you get 9x =9??!!!
9x would be equal to 8.991
Therefore X = .999
You've obviously made a mistake, you can check this on a normal calculator.
[edit on 17-4-2005 by PeteTPP]


Pete, if you go back and reread the first post, it clearly says that whenever .999 is used, .9 repeater is meant.
Here is the post that convinced me that they are indeed equal:

quote: Originally posted by BlackGuardXIII
'If I divide 9 into 1 I get .1 repeating........Divide 1 into 1 = 1, not .9 repeating.'
and,
"multiply 1/9 * 9 you get 1
multiply .1 repeating * 9 you get .9 repeating
if you accept 1/9 equals .1 repeating, then you must accept that 1 = .9 repeating because of the Multiplicative Identity law of mathematics."
[edit on 4/3/2005 by djohnsto77]



posted on Apr, 21 2005 @ 10:57 AM
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Originally posted by BlackGuardXIII
quote: Originally posted by BlackGuardXIII
'If I divide 9 into 1 I get .1 repeating........Divide 1 into 1 = 1, not .9 repeating.'
and,
"multiply 1/9 * 9 you get 1
multiply .1 repeating * 9 you get .9 repeating
if you accept 1/9 equals .1 repeating, then you must accept that 1 = .9 repeating because of the Multiplicative Identity law of mathematics."
[edit on 4/3/2005 by djohnsto77]


If you cannot accept that 1/9 is EQUAL to .1 repeating. You can only state it is APPROX. .1 repeating because there is no definite value for 1/9. Therefore by the identity you can only say that 1 is APPROX. .9 repeating because of the same concept.



posted on Apr, 21 2005 @ 11:56 AM
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i don't know why people have such touble realising that 1/9=0.1111~ (repeating forever and ever) it is an equals sign, they are exactly equal, 100% the same thing, if there was a difference then there would be a very serious flaw in mathematics.

I don't mean this to sound condescending or anything but if you can't imagine infinity and what an infinity of recurring digits is then you cannot hope to understand in a fundamental way why .999~ = 1, unless it is just obvious to you.



posted on Apr, 21 2005 @ 03:26 PM
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So your trying to say that any prime number

(even though 9 is not a prime number, but it does work because it's only other multiple is a prime number)

lets say 11, divide 1 by this prime..... 1/11 = .0909 on and on infinity times.

(imagining infinity...) ok 1/11 = .0909090909.....

times 11 will equal 1.

Doesn't work that way, the only way it works is because your calculator is built to round off.

Once again, there is no real value for fractions of 1 divided by a prime number. It's kind of a paradox lol Your trying to imagine infinity .1111's but infinity is not tangible and then trying to say they are equal to each other.

Here's an activity imagine infinite .1111, times that by nine (and forget about the incorrect 1/9 = .1111 thing) it will never equal 1.

[edit on 21-4-2005 by Aether]



posted on Apr, 21 2005 @ 05:34 PM
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Doesn't work that way, the only way it works is because your calculator is built to round off.


sorry but it does work that way.
The fact that .999~ recurring (this seems to be the word you don't appreciate) is 100%, absolutely, true, it is indisputible fact. If it isnt equal to one then there would be a number between it and 1, can you show me this number?

There have now been several proofs of this on this thread, limits of functions, using set theory, convergent sequences, if you can point out the flaw in any of them i'd be happy to try and show you how the flaw you point is not a flaw.

Also, what do primes and calculators rounding numbers have to do with anything?



posted on Apr, 22 2005 @ 02:09 AM
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There have now been several proofs of this on this thread, limits of functions, using set theory, convergent sequences, if you can point out the flaw in any of them i'd be happy to try and show you how the flaw you point is not a flaw.

Also, what do primes and calculators rounding numbers have to do with anything?
cmdrpaddy

I agree, and am glad that I learned something here. It may be that some of the posters who cannot see the logic are more inclined to excel in areas other than mathematics. Either that or they may not have read all the posts. It is certainly clear to me now. I started off quite firmly convinced that .9 and 1 were not equal. Now I am of the view that they are.

Re: Prime numbers, calculators, and rounding off.... the only thing I can think of is that mentioning them sounds informed. If you have a calculator that can express 20 digit products, it is a fun exercise to multiply 111 111 111 by 111 111 111. The answer may amuse you.

[edit on 03 22 2005 by BlackGuardXIII]



posted on Oct, 22 2007 @ 04:04 AM
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just as a small footnote to all of this, i'm NOT even close to a mathematician, but. i spotted a post very early on with some pretty complex maths into it, and i drew a simple question from a piece of it.

If three thirds make a whole (lets consider a basic circle)

1/3 = 0.333 recurring

2/3 = 0.666

therefore..

3/3 = 0.999

see where i'm goin with this? Just something simple that i've never thought of. Would this mean that there is no such thing as a 'complete circle'? Regardless of how close .999 gets, it'll never quite make it. It's like no matter how good looking i get, I'll never get Jessica Alba!


Seriously though, try and explain it. I'll bet it's simple, but I've no head for numbers!



posted on Oct, 22 2007 @ 05:15 AM
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The simplest way to see that 0.9999... = 1 is to try to work out the difference between 0.999... and 1. Clearly there isn't a differnce: any number you could suggest for 1 - 0.999... is too large, so the answer must be zero.

The reasoning is the same as why you can't count to infinity - what number would you count immediately before reaching infinity?



posted on Oct, 23 2007 @ 04:34 AM
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Originally posted by electric
I believe .9 recurring could be expressed as a fraction of infinity.


old thread, but I guess I'll respond to this I missed so long ago...

When I said a rational number has to be able to be expressed as a fraction, I meant a fraction of two integers.

∞, π, e, i, or even √2 etc. don't count.




[edit on 10/23/2007 by djohnsto77]




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