0.9999....(recurring) = 1?

Ricky · 2007-03-07 19:34:34

Plus, you can write out only a finite amount of 9's forever.

You contradicted yourself. If there are a finite amount of 9's, then there must exist some integer n that n > the number of 9's. But since n is fixed and you are writing them forever, you will one day surpass n. Contradiction.

George,Y · 2007-03-07 19:34:59

Ricky wrote:

George, you restrict yourself from the wonders of math by sticking with what can only be done in reality. And before you say that math should be based on reality again, I ask you once again, where is infinity in reality?
Just because you can't physically write them out doesn't mean you can't talk about what it would be if you could.

Are you accusing yourself for preventing me to have the last, the rightended, the infiniteth 9 by just the fact that they(it) don't(doesn't) exist in reality?!

George,Y · 2007-03-07 19:36:30

Ricky wrote:

Plus, you can write out only a finite amount of 9's forever.
You contradicted yourself. If there are a finite amount of 9's, then there must exist some integer n that n > the number of 9's. But since n is fixed and you are writing them forever, you will one day surpass n. Contradiction.

No, not, I said "if you don't", haven't I?

I only explored both your choices, isn't that correct?

I really doubt your patience to finish reading my posts.

Ricky · 2007-03-07 19:36:33

George,Y wrote:

Ricky wrote:
George, you restrict yourself from the wonders of math by sticking with what can only be done in reality. And before you say that math should be based on reality again, I ask you once again, where is infinity in reality?
Just because you can't physically write them out doesn't mean you can't talk about what it would be if you could.
Are you accusing yourself for preventing me to have the last, the rightended, the infiniteth 9 by just the fact that they(it) don't(doesn't) exist in reality?!

No George, it doesn't exist in math. I've shown this over an over again, simply because the digits of a real number are countable.

Ricky · 2007-03-07 19:38:30

No, not, I said "if you don't", haven't I?
I only explored both your choices, isn't that correct?
I really doubt your patience to finish reading my posts.

I'm sorry, but this doesn't make any sense. Where did you say, "if you don't"? What choices?

George,Y · 2007-03-07 19:52:11

I am sorry for word mistake. But the second of your questions can go back to Post 540. "If you deny" -change it a little bit, you deny you can finish counting or writting 9's.

The first problem:

Let's see where your contradiction really lies. Another reason for the existence of the smallest 9:
Every 9 except the first one is smaller than the the one at its left. The bunch is static and not growing, so the one on the right end is the one smallest. Now contradiction: this 9 cannot stand for any finite amount , otherwise its not the last. Then infinitesimal and the question on where infinitesmall begins emerges. So you have just changed the contradiction of infinitesimal into my smallest 9 seemingly contradiction by denying the existence of the 9 on the right end.

George,Y · 2007-03-07 19:53:38

How did you deny it? By "you cannot write or remove to that"!
Still the double standards.

Ricky · 2007-03-07 19:58:35

The bunch is static and not growing, so the one on the right end is the one smallest.

How can you talk about a right end? There are an infinite number of them, and thus, no right end.

George,Y · 2007-03-07 20:11:48

There are an infinite number of them, and thus, no right end.

Why thus?!

Because you cannot count to the right end?

no

Because infinte means endless?

endless means growing. If it is static then you are able to get to the right end, like the right end B of line segment AB. Can you have something that is both static and endless?

So I don't know whether your endless/growing infinite starts from finite 9's or infinite 9's, if the former, you know the consequence. If having got infinite amount of 9's already but the 9's are relentlessly endlessly increasing (or simply more than static infinite 9's) please check my second structure (yes it's especially designed for you, you are my VIP).

Last edited by George,Y (2007-03-07 20:13:15)

lightning · 2007-03-07 20:13:56

cool

Ricky · 2007-03-07 20:16:39

endless means growing.

No, it does not. The integers endless. Are they growing? No. In geometry, is a line in space growing? No. Is it endless? Yes.

Just because something has no end does not mean it grows.

lightning · 2007-03-07 20:18:30

as i said cool!

George,Y · 2007-03-07 21:06:11

Ricky wrote:

No, it does not. The integers endless. Are they growing? No. In geometry, is a line in space growing? No. Is it endless? Yes.

No, because when you say natural numbers s are endless, you list them {1,2,3,4,...} you are counting from 1,2 untill a stop like 10 or 15, and you guess you can keep on counting to get the "endless"(endless means not stop counting here) set of "All" integers, but infact you cannot get the set by counting. And so long as the counting is still "on", the set is non-static but expanding, endlessly. Endless mean the same as the ability to resume counting here. So the property "endless" still comes from counting. Counting is not a static thing.

How do you draw a line? Geometry teacher might have taught you how to draw a line. He wanted to draw it fading to the left as well as fading to the right. It means endless.

The only thing static you can get is the already drawed line segment and the direction of it. This direction can be termed as static. But if the length or the quazi-length of the line is static, it's infinity. In that way you can make the line an axis. And the length of the axis is infinity. Scale the axis, you shall mark infinity/2 to the right side of line segment representing the line on your paper, and mark -infinity/2 to the left side of it. Because you admit the length is staticly infinity. In this way you admit infinity is included in the Reals. And this infinity should not be interpreted as only a growing variable, which contradicts the static assumption.

So the only way that the line can exist in maths is the way that it is a direction fixed, expanding line segment.

Last edited by George,Y (2007-03-07 21:08:41)

George,Y · 2007-03-07 21:12:36

OK, forget about it.

Does endless="more and more"?
Philosophical proof:
If no more, then boundary, meaning end. not endless. (endless=> more and more)
If end, then no more.(more and more=>endless)

And the length of the line delima shall still apply, substitute the growing by no more.

Last edited by George,Y (2007-03-07 21:26:58)

George,Y · 2007-03-07 22:22:09

Addition to Post 564, if the line has already a length of infinity, it has got at least two points the distance between which is infinity. Every line is equivalent to an axis, written by maths textbook. Every point on an axis has a "real number" distance from the origin, the two points' distances from the origin are infinity. So infinity is a real number.

Contradiction even to your orthodoxy maths, haha...

If the amount of elements of the natural number set {1,2,3,...} is not growing finitely, instead, it's constant. It must be infinity. The amount of elements of this set must equate the end element of the set, because of the one to one relationship of them. So Infinity is included in you natural number set.

mathsyperson · 2007-03-07 22:49:14

George, you're right. Counting is not a static thing.
However, the point that you're missing is that while "the highest number that you have counted to" is perfectly capable of growing, "the highest number" is not.

Your assertation that something that is endless must be growing can be disproved with the simple counter-example of a circle. In addition, lines can be thought of as circles with no curvature.

George,Y · 2007-03-08 00:00:56

I am currently working on the endless=more and more parts concept. However, I shall exclude your circle in my particular type of endless and tell the reason behind it.

Anyway, Post 564 holds, do you agree?

My brain is tired... I may rest for a couple of days...

Anthony.R.Brown · 2007-03-08 00:34:30

---------------------------------------------------------------------------------------------------------------
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 "

---------------------------------------------------------------------------------------------------------------
RECURRING DEFINITION PROOF 03/03/07 by Anthony.R.Brown.
---------------------------------------------------------------------------------------------------------------

The Definition for Recurring is given below..............................................................................

A Number that repeats itself Endlessly! Continuously repeating the same Number!

Below are examples of Recurring Numbers! They are of course Endless! Length is example only!

Recurring ( 0.1 ) = .111111111111111111111111111111111111111111111111111111111111111

Recurring ( 0.2 ) = .222222222222222222222222222222222222222222222222222222222222222

Recurring ( 0.3 ) = .333333333333333333333333333333333333333333333333333333333333333

Recurring ( 0.4 ) = .444444444444444444444444444444444444444444444444444444444444444

Recurring ( 0.5 ) = .555555555555555555555555555555555555555555555555555555555555555

Recurring ( 0.6 ) = .666666666666666666666666666666666666666666666666666666666666666

Recurring ( 0.7 ) = .777777777777777777777777777777777777777777777777777777777777777

Recurring ( 0.8 ) = .888888888888888888888888888888888888888888888888888888888888888

Recurring ( 0.9 ) = .999999999999999999999999999999999999999999999999999999999999999

The above examples are shown to be True! in the Calculations below! According to the Definition for Recurring!

( 0.1 ) Recurring < 1 and <> 1

( 0.2 ) Recurring < 1 and <> 1

( 0.3 ) Recurring < 1 and <> 1

( 0.4 ) Recurring < 1 and <> 1

( 0.5 ) Recurring < 1 and <> 1

( 0.6 ) Recurring < 1 and <> 1

( 0.7 ) Recurring < 1 and <> 1

( 0.8 ) Recurring < 1 and <> 1

( 0.9 ) Recurring < 1 and <> 1

---------------------------------------------------------------------------------------------------------------
INFINITE 0.9 <> 1 PROOF : THE INFINITE 10 % PERCENT DIFFERENCE 03/03/07
by Anthony.R.Brown.
---------------------------------------------------------------------------------------------------------------
One of the most Accurate and sound ways to prove Infinite 0.9 <> 1 is to give the Infinite Percent Difference Values from the Start Onwards!

The example below is for the first Ten Decimal Place's,which clearly shows the count increasing as more and more Infinite .9's are looked at! But remain a constant Difference of 10% in relation to how far the example has traveled.

Count = ...... ( 1 ).....( 2 )....( 3 )...( 4 )....( 5 )...( 6 )....( 7 )....( 8 )....( 9 ).....( 10 )

Infinite 10 %
Difference =..(10%).(10%).(10%).(10%).(10%).(10%).(10%).(10%).(10%)...(10%)

Infinite 0.9 = ( 0.9 ) ( 1.8 ) ( 2.7 ) ( 3.6 ) ( 4.5 ) ( 5.4 ) ( 6.3 ) ( 7.2 ) ( 8.1 ) ( 9 )

................... ( x 1 ) ( x 2 ) ( x 3 ) ( x 4 ) ( x 5 ) ( x 6 ) ( x 7 ) ( x 8 ) ( x 9 ) ( x 10 )

Infinite 0.9 Onwards! there will always be a 10 % Difference making it Impossible for Infinite 0.9 to ever = 1

---------------------------------------------------------------------------------------------------------------

p.s This is my last Post on this so called Math forum! unless the Post title is Changed to something that is not BIASED!

The Moderators! and Admin should only be Referees! and not have any Personnel Opinions on the Math subjects! and especially not allow titles like this! that straight from the Start are clearly expressing a BIASED View!

Bye from A.R.B ..................................................................................................................

Maelwys · 2007-03-08 01:25:06

Anthony.R.Brown wrote:

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 "

This proof has been countered many times, and you've still yet to raise a coherant defense for it.

Anthony.R.Brown wrote:

( 0.1 ) Recurring < 1 and <> 1
( 0.2 ) Recurring < 1 and <> 1
( 0.3 ) Recurring < 1 and <> 1
( 0.4 ) Recurring < 1 and <> 1
( 0.5 ) Recurring < 1 and <> 1
( 0.6 ) Recurring < 1 and <> 1
( 0.7 ) Recurring < 1 and <> 1
( 0.8 ) Recurring < 1 and <> 1
( 0.9 ) Recurring < 1 and <> 1

This quote has also been rebuttled above.

Anthony.R.Brown wrote:

---------------------------------------------------------------------------------------------------------------
INFINITE 0.9 <> 1 PROOF : THE INFINITE 10 % PERCENT DIFFERENCE 03/03/07
by Anthony.R.Brown.
---------------------------------------------------------------------------------------------------------------
One of the most Accurate and sound ways to prove Infinite 0.9 <> 1 is to give the Infinite Percent Difference Values from the Start Onwards!
The example below is for the first Ten Decimal Place's,which clearly shows the count increasing as more and more Infinite .9's are looked at! But remain a constant Difference of 10% in relation to how far the example has traveled.
Count = ...... ( 1 ).....( 2 )....( 3 )...( 4 )....( 5 )...( 6 )....( 7 )....( 8 )....( 9 ).....( 10 )
Infinite 10 %
Difference =..(10%).(10%).(10%).(10%).(10%).(10%).(10%).(10%).(10%)...(10%)

Infinite 0.9 = ( 0.9 ) ( 1.8 ) ( 2.7 ) ( 3.6 ) ( 4.5 ) ( 5.4 ) ( 6.3 ) ( 7.2 ) ( 8.1 ) ( 9 )
................... ( x 1 ) ( x 2 ) ( x 3 ) ( x 4 ) ( x 5 ) ( x 6 ) ( x 7 ) ( x 8 ) ( x 9 ) ( x 10 )
Infinite 0.9 Onwards! there will always be a 10 % Difference making it Impossible for Infinite 0.9 to ever = 1

I don't even understand this one... there's a 10% difference between what? 0 and 9? And where did the 1.8, 2.7, etc, come from? I'm thoroughly confused, sorry.

Anthony.R.Brown wrote:

p.s This is my last Post on this so called Math forum! unless the Post title is Changed to something that is not BIASED!
The Moderators! and Admin should only be Referees! and not have any Personnel Opinions on the Math subjects! and especially not allow titles like this! that straight from the Start are clearly expressing a BIASED View!

The title was already changed to be unbiased. It's now a question of whether or not 0.999... = 1, open for discussion on whether or not it's true.

lightning · 2007-03-08 05:38:10

your better [probaly] like a calculator

Ricky · 2007-03-08 06:08:14

George, I think we need to start from the basics. Let me know if you disagree with anything in this:

Let

Then A may be represented by the sequence:

Every term in this sequence can be labeled by an element in the natural numbers. As there is no infinity in the natural numbers, there is no "infiniteth" element.

lightning · 2007-03-08 06:16:14

yep

kylekatarn · 2007-03-08 12:47:36

George,Y · 2007-03-08 13:23:56

Ricky wrote:

George, I think we need to start from the basics. Let me know if you disagree with anything in this:
Let
Then A may be represented by the sequence:
Every term in this sequence can be labeled by an element in the natural numbers. As there is no infinity in the natural numbers, there is no "infiniteth" element.

No, don't try to hide your growing series or your counting into a bracket.

George,Y · 2007-03-08 13:39:15

Substraction alone can find the last 9.

This is my last post on this thread. I am not going to spend my time on this forever. Bye, everyone!

Math Is Fun Forum

#551 2007-03-07 19:34:34

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

#552 2007-03-07 19:34:59

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

#553 2007-03-07 19:36:30

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

#554 2007-03-07 19:36:33

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

#555 2007-03-07 19:38:30

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

#556 2007-03-07 19:52:11

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

#557 2007-03-07 19:53:38

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

#558 2007-03-07 19:58:35

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

#559 2007-03-07 20:11:48

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

#560 2007-03-07 20:13:56

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

#561 2007-03-07 20:16:39

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

#562 2007-03-07 20:18:30

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

#563 2007-03-07 21:06:11

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

#564 2007-03-07 21:12:36

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

#565 2007-03-07 22:22:09

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

#566 2007-03-07 22:49:14

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

#567 2007-03-08 00:00:56

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

#568 2007-03-08 00:34:30

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

#569 2007-03-08 01:25:06

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

#570 2007-03-08 05:38:10

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

#571 2007-03-08 06:08:14

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

#572 2007-03-08 06:16:14

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

#573 2007-03-08 12:47:36

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

#574 2007-03-08 13:23:56

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

#575 2007-03-08 13:39:15

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

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