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#126 2006-11-27 04:30:46

Ricky
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Registered: 2005-12-04
Posts: 3,791

Re: 0.9999....(recurring) = 1?

Anthony, your concept of decimal expansion is way off.  It has nothing to do with "making something bigger".  0.999... is not smaller than 1.  Real numbers are static, they don't grow or change.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#127 2006-11-27 04:48:47

luca-deltodesco
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Registered: 2006-05-05
Posts: 1,470

Re: 0.9999....(recurring) = 1?

to be honest, i think the proof:





is good enough without going into all this other math thats been mentioned.

Last edited by luca-deltodesco (2006-11-27 04:49:13)


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#128 2006-11-28 02:07:54

Anthony.R.Brown
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Posts: 516

Re: 0.9999....(recurring) = 1?

To luca-deltodesco

I am sorry but you cannot multiply an Infinite by 10 or change an Infinite Number!

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#129 2006-11-28 03:38:24

luca-deltodesco
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Registered: 2006-05-05
Posts: 1,470

Re: 0.9999....(recurring) = 1?

is not infinity, nor is it an infinate number.

put it this way

means in laymans terms, a 0. followed by an infinite number of 9's, so if you multiply this number by 10, you shift the decimal point one place to the right, and you get 9, followed by an infinite number of 9's, if you then take away the first number, every single 9 after the decimal point in the second number, is cancelled out by the 9's after the decimal point in the first number, and you're left with 9.

Last edited by luca-deltodesco (2006-11-28 03:40:19)


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#130 2006-11-29 00:38:23

Anthony.R.Brown
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Re: 0.9999....(recurring) = 1?

To luca-deltodesco!

The problem is it's impossible to know how many 9's there are in total!! because it's an Infinite Number! ie No End!.............................................................................................................

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#131 2006-11-29 03:01:05

luca-deltodesco
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Posts: 1,470

Re: 0.9999....(recurring) = 1?

how is that a problem?


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#132 2006-11-29 05:45:26

Ricky
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Re: 0.9999....(recurring) = 1?

Anthony wrote:

The problem is it's impossible to know how many 9's there are in total!!

Then wrote:

because it's an Infinite Number!

That is the number of 9's.  Non-finite.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#133 2006-11-29 09:14:16

Devantè
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Registered: 2006-07-14
Posts: 6,400

Re: 0.9999....(recurring) = 1?

I just use:





When asked a question like this.

It's arguable, so I'm not saying that it's the absolute certain proof.

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#134 2006-11-29 10:02:17

luca-deltodesco
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Registered: 2006-05-05
Posts: 1,470

Re: 0.9999....(recurring) = 1?

tbh, i dont understand how anyone can argue this simple proof? you get people saying, oh but when you times it by 10, there must be on less 9 on the end of it, but that doesnt make sense, because thats treating infinity as a definate value.


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#135 2006-11-29 10:17:16

Ricky
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Re: 0.9999....(recurring) = 1?

luca, the proof makes assumptions about binary operations performed on the decimal expansion of real numbers.  Those assumptions turn out to be correct based on most standard definitions, but they are presented as assumptions none the less.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#136 2006-11-30 00:56:22

Anthony.R.Brown
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Posts: 516

Re: 0.9999....(recurring) = 1?

If all Infinite Numbers equalled an Integer Number as in Infinite 0.9 = 1 it would be much easier to just call them Integer Numbers!!

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#137 2006-11-30 05:19:16

Ricky
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Registered: 2005-12-04
Posts: 3,791

Re: 0.9999....(recurring) = 1?

0.999... is an integer!


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#138 2006-12-01 02:05:56

Anthony.R.Brown
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Re: 0.9999....(recurring) = 1?

To Ricky!

But how can any Number become! or is an Integer Number if it starts as . < 1

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#139 2006-12-01 05:47:24

Ricky
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Registered: 2005-12-04
Posts: 3,791

Re: 0.9999....(recurring) = 1?

But how can any Number become! or is an Integer Number if it starts as . < 1

But that statement isn't true.  There is a theorem which says:



In other words, if I have two numbers:

0.375.... (note that ... here means I know there are other digits, but I don't know what they are)

and

0.376.... (same thing here)

Without knowing any other digits, I can state that 0.375... <= 0.376 but I can not state that 0.375... < 0.376...


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#140 2006-12-02 03:22:59

Anthony.R.Brown
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Posts: 516

Re: 0.9999....(recurring) = 1?

To Ricky!

Its Quite simple! I can also state that any number that has a . at the start! before the second part of the number! will always be smaller than 1
as in Infinite .9 will always be smaller than 1

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#141 2006-12-02 07:16:21

Ricky
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Registered: 2005-12-04
Posts: 3,791

Re: 0.9999....(recurring) = 1?

Its Quite simple! I can also state that any number that has a . at the start! before the second part of the number! will always be smaller than 1

Sure, you can state that.  But you'd be wrong.  I've tried to explain how in as many ways as possible.  (At least) Three different proofs have been in these threads show that 0.999... = 1, and you have yet to level one criticism against any of them.  You just keep stating that 0.999... does not equal 1.  Frankly, I feel like I'm talking to a brick wall, and I'm getting tired of it.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#142 2006-12-03 02:14:01

Anthony.R.Brown
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Registered: 2006-11-16
Posts: 516

Re: 0.9999....(recurring) = 1?

To Ricky!

QUOTE:  "I feel like I'm talking to a brick wall, and I'm getting tired of it."

This is a good point! at the end? of the Universe! and at the end? of an Infinite Number! there is a BRICK WALL! but unfortunatly behind the BRICK WALL! is an endless stream of .9's

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#143 2006-12-03 02:36:15

Toast
Real Member
Registered: 2006-10-08
Posts: 1,321

Re: 0.9999....(recurring) = 1?

This thread is a brick wall.

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#144 2006-12-03 02:55:20

Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400

Re: 0.9999....(recurring) = 1?

I'm a brick wall.

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#145 2006-12-03 05:26:39

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: 0.9999....(recurring) = 1?

i completely agree with ricky hmm


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#146 2006-12-05 01:34:40

Anthony.R.Brown
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Posts: 516

Re: 0.9999....(recurring) = 1?

Genius! is seen in the eyes of others! when the problem is made clear! by the Genius!

A.R.B

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#147 2006-12-05 01:42:07

Patrick
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Registered: 2006-02-24
Posts: 1,005

Re: 0.9999....(recurring) = 1?

Anthony - how about you start to prove the proofs false instead of writing nonsense


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#148 2006-12-05 05:40:12

Ehiness
Member
Registered: 2006-12-05
Posts: 6

Re: 0.9999....(recurring) = 1?

I know this has probably been said before but:




-

-

-

and so by the same steps:




-

-

-

(did I make any mistakes in the proof?)

Last edited by Ehiness (2006-12-05 05:51:27)

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#149 2006-12-06 02:08:11

Anthony.R.Brown
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Registered: 2006-11-16
Posts: 516

Re: 0.9999....(recurring) = 1?

OK LET'S SEE IF SOMEONE CAN REALLY PROVE THIS QUESTION!



Infinite 0.9 (stage one) the start! = 0.9 that is a 0 then a . then a 9 (this is the first .9)



If anyone can? using time a guide to how far the calculations have run,prove that Infinite 0.9 = 1 ?



0.9999999999999999999999999999999......



Ok! for every .9 above I am going to use (1) second of time!



So now give me! using time how long it will take for Infinte 0.9 to = 1



Example below!



0.9 = (1 second) 0.99 = (2 seconds) 0.999 = (3 seconds) etc.........................

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#150 2006-12-06 03:06:23

Patrick
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Registered: 2006-02-24
Posts: 1,005

Re: 0.9999....(recurring) = 1?

That doesn't even make sense... Why would you do that? You can't keep on counting and eventually reach infinity. It's not a point, like the wall you described.


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