INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

Anthony.R.Brown · 2007-02-15 02:44:46

[ By posting this theory here, you willingly allow others to discuss the point in a civilized manner. Moderator action has been taken against those who are not civilized by Ricky and Zach. ]

INFINITE 0.9 <> 1 PROOF By,Anthony.R.Brown,15/01/07.

The Variables below A & B are Both Single Start Values.

A = 1

B = 0.9

Below Proves A is Infinitely > B And Gives The Variable C This Value.

C = A / B = 1.1111111111......

Below is How Infinite 0.9 is Calculated.

0.9 x C = 0.9999999999 ......

Below Proves Infinite 0.9 is <>1 By Using The Original Variables A & B.

A x C = 1.1111111111 ......

B x C = 0.9999999999 ......

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

The Variables below A & B are Both Single Start Values.

A = 1 "This has to be the Start Value for 1"

B = 0.9 "This has to be the Start Value for Infinite 0.9"

C = A / B = 1.1111111111......

A x C = 1.1111111111 ......"This is the same Calculation to Make a Number Infinite! as with B"

B x C = 0.9999999999 ......"This is now Infinite 0.9"

The two Values for A and B are different! because Infinite 0.9 <> 1

If the Result for A did Equal B then Infinite 0.9 does = 1

Even If! by some Magic B does become 1 it wil still be Infinite 0.11111..... Less than A
----------------------------------------------------------------------------------------------------------------

A starts as = 1

B starts as = 0.9

A x C results in a number > 1

B x C results in a number < 1

The point is A is 1

and B never = 1

If we are going to Infinitely multiply a number so that is becomes 1 "if possible"

Then a number that is already 1 must always be Greater!!
----------------------------------------------------------------------------------------------------------------
A starts as = 1
B starts as = 0.9
A x C results in a number > 1
B x C results in a number < 1
The point is A is 1
and B never = 1

If we are going to Infinitely multiply a number so that it becomes 1 "if possible"

Then a number that is already 1 must always be Greater
----------------------------------------------------------------------------------------------------------------

A x C = 1.11111...

B x C = 0.99999....

It Only takes One Calculation for A x C to = 1.1111.....Because A is! and A eqauls 1

It takes B x C to = 0.9999999..... Which is One Calculation Because B is < 1 to start with!

If B was Now to Some how now Reach! or Equal 1 by Multiplication! this would only then = 1

This would be would still make B 0.1 < A because B never started as 1 or = 1 the same as A
----------------------------------------------------------------------------------------------------------------

LET'S MAKE THIS AS CLEAR AS POSSIBLE! USING NEW VARIABLES.

N1 = 0.9 This is a Single Number Value

N2 = Infinite 0.9 This is an Infinite Number!

N3 = 1 This is a Single Number Value

N1..............( Here between N1 and N3 there are no other Numbers! Because N1 is the Single last Number!).............N3.

N2..............( Here between N2 and N3 there are an Infinite Amount of Numbers! Because N2 is an
Endless stream of Numbers!).............N3.
----------------------------------------------------------------------------------------------------------------

If a Number has to be Infinitely Multiplied! To Try and Reach a Target Value! Then the Target Value! Must be Greater than the Number being Infinitely Multiplied! Reason Being! If the Target Value was also Infinitely Multiplied! Then the Target Value would again be Greater!
Number Infinitely Multiplied! = 0.9 Target Value! = 1

[Anthony.R.Brown 20/01/07
----------------------------------------------------------------------------------------------------------------

I would now like to Add another Variable to this Example! N4

This is for anyone who feels it's not possible to place another Number between N2 and N3.

N4 = The Maximum possible Number of .9's

Anyone who feels its not possible to place another Number between N2 and N3, all they have to do to prove how they feel! Is giving a Value for N4.

So now we have!.....

N2..............( Here between N2 and N3 there are an Infinite Amount of Numbers! Because N2 is an
Endless stream of Numbers!).............N3.

N2..............( How Ever! If..N4...is proved! Then the above is not True!).............N3.

N2..............( But as it Stands!..N4...Can have + .9's i.e More .9's Between! Because N2 is Infinite!).............N3.
----------------------------------------------------------------------------------------------------------------

LET'S MAKE THIS EVEN MORE CLEARER!

N1 = 0.9 This is a Single Number Value

N2 = Infinite 0.9 This is an Infinite Number!

N3 = 1 This is a Single Number Value

N4 = The Maximum possible Number of .9's ?

N1..............( Here between N1 and N3 there are no other Numbers! Because N1 is the Last Single Number! Before ).............N3.

N2..............( Here between N2 and N3 there are an Infinite Amount of Numbers! Because N2 is an Endless stream of Numbers! Before ).............N3.

Below if Anyone can Give! and Prove! a Value for N4 Then the Above will be False! and not True! for then another .9 will not be able to be Inserted Between N2..and..N3.

N2..............(.N4.)...........N3.
----------------------------------------------------------------------------------------------------------------

N1 = 0.9 This is a Single Number Value And Yes! .9 is The Last Digit! Because its not an
Infinite Number the same as N2

N4 is the Variable to Represent the .9,s which is Between N2 and N3
Because N4 is an Infinite number then Any amount of .9,s can be Inserted to Represent N4
Unless! " Anyone can Give! and Prove! a Value
----------------------------------------------------------------------------------------------------------------

N1 = 0.9 This is a Single Number Value

and is the last Single Value then 0.2,0.3,0.4,0.5,0.6,0.7,0.8, Then N1 and Then 1
----------------------------------------------------------------------------------------------------------------

Below is Needed because No One! is prepared to put forward an Example,in a line by line way! the same as my Proof! to explain what they are trying to say!
The main problems are not saying at what stage A & B are at! i.e Single Start Values! or Calculated x C.
I am going to Add some new Variables so everyone knows what is Happening!
Sometimes new Variables have to be Add to explain things in an easier way,a good example is the N2 = Infinite 0.9999..."is it possible to insert anymore Numbers Between! " N3 = 1
as soon as I introduced the N4 Variable = The Maximum possible Number of .9's ?
Everyone was stumped! Because as they know as soon as anyone gives a Value for N4,I will answer with N2..............(.N4 + "as many more .9s I want to Insert!.)...........N3.

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

INFINITE 0.9 <> 1 PROOF By,Anthony.R.Brown,29/01/07.

The Variables below A1 & B1 are Both Single Start Values.

A1 = 1 "This has to be the Start Value for 1"

B1 = 0.9 "This has to be the Start Value for Infinite 0.9"

C = A1 / B1 = 1.1111111111...."There is only one Value & Variable for C"

A2 = A1 x C = 1.1111111111 ......"This is the same single Calculation as B2"

B2 = B1 x C = 0.9999999999 ......"This is now Infinite 0.9 and a single Calculation"

If B1 or B2 was at anytime to = A1 Then either would end up with the same Result as A2,but because it will take more than one single Calculation! for B1 or B2 to = A1
Then its Impossible from the Start for Infinite 0.9 to ever = 1 in a single Calculation.
----------------------------------------------------------------------------------------------------------------
INFINITE 0.9 <> 1 PROOF By,Anthony.R.Brown,02/02/07.
----------------------------------------------------------------------------------------------------------------

( 1.1 ) x 0.9 = 0.99 " One Decimal Place = " 0.1 < 1

( 1.11 ) x 0.9 = 0.999 " Two Decimal Place's = " 0.1 < 1

( 1.111 ) x 0.9 = 0.9999 " Three Decimal Place's = " 0.1 < 1

( 1 / 0.9 ) x 0.9 = 0.9..... " Infinite Decimal Place's = " 0.1 < 1 "

The 0.1 Difference Above is Permanent! Because it is an Infinite Difference!!

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

To Back up my Proof above! I would like to Make an Immortal Quote:

" IF TWO NUMBERS START WITH A DIFFERENCE IN THEIR VALUES! AND BOTH ARE MULTIPLIED BY THE SAME AMOUNT! ONE VALUE WILL ALWAYS BE GREATER THAN THE OTHER!! "
----------------------------------------------------------------------------------------------------------------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
----------------------------------------------------------------------------------------------------------------

I thought I made it Clear!

V1 = 0.99999999999999999999999999999999..Infinite.0.9...." = The 0.9 Value from the Start Onwards! "

V2 = 0.00000000000000000000000000000000..Infinite.0.1...." = The < 1 Value from the Start Onwards! "

V1 = Infinite 0.9

V2 = The Infinite Difference

No Matter how Long V1 is! V2 will always be the same Length!

Because V1 starts as 0.9 and Because V2 starts as 0.1 The Difference will always be the same!
----------------------------------------------------------------------------------------------------------------
INFINITE 0.9 <> 1 PROOF : TRUTH TABLE : By,Anthony.R.Brown,07/02/07.
----------------------------------------------------------------------------------------------------------------Below V1 = The Infinite 0.9 Sequence. : Below V2 = The < 1 Infinite Difference Sequence.

V1 = ( 0.9 ) + V2 = ( 0.1 ) = 1

V1 = ( 0.99 ) + V2 = ( 0.01 ) = 1

V1 = ( 0.999 ) + V2 = ( 0.001 ) = 1

V1 = ( 0.9999 ) + V2 = ( 0.0001 ) = 1

V1 = ( 0.99999 ) + V2 = ( 0.00001 ) = 1

V1 = ( 0.999999 ) + V2 = ( 0.000001 ) = 1

V1 = ( 0.9999999 ) + V2 = ( 0.0000001 ) = 1

V1 = ( 0.99999999 ) + V2 = ( 0.00000001 ) = 1

V1 = ( 0.999999999 ) + V2 = ( 0.000000001 ) = 1

V1 = ( 0.9999999999 ) + V2 = ( 0.0000000001 ) = 1

The Table above clearly shows no matter how long V1 is! it will always need the algebra + symbol for V1 to equal 1 ( V1 + V2 ) = 1

This proves Infinite 0.9 <> 1 because if ( V1 + V2 ) = 1 is allowed! it will be a contradiction to the term Infinite 0.9.

----------------------------------------------------------------------------------------------------------------
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!!

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INFINITE 0.9 <> 1 PROOF : THE INFINITE 10 % PERCENT DIFFERENCE 03/03/07
by Anthony.R.Brown.
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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

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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 "

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Last edited by Anthony.R.Brown (2007-03-04 03:46:29)

Zach · 2007-02-23 12:36:41

[ I have removed all other posts from this thread because none of them were revelant to the actual topic. They only debunked the post with crude arguements and no proofs. If you wish to make further posts on this topic, do so in a civilized manner in which you are discussing the theory. If you wish to disprove the theory, do not use insults or act hostile. This is a forum dedicated to learning, understanding and development, not saying "YOU'RE WRONG" without any back-up. If you continue to act the way you did, I will take strong action. ]

MathsIsFun · 2007-02-23 16:24:29

Thank you Zach. It is worth pointing out proofs FOR 0.999... = 1 presented here: http://www.mathsisfun.com/forum/viewtopic.php?id=5700

Anthony.R.Brown · 2007-02-25 00:57:09

To keep everything Fare again! can all other Posts not to do with this Post! be removed again! including the Link above! to the other Post!

A.R.B

luca-deltodesco · 2007-03-02 04:14:39

Anthony.R.Brown wrote:

The Variables below A & B are Both Single Start Values.
A = 1
B = 0.9
Below Proves A is Infinitely > B And Gives The Variable C This Value.
C = A / B = 1.1111111111......
Below is How Infinite 0.9 is Calculated.
0.9 x C = 0.9999999999 ......
Below Proves Infinite 0.9 is <>1 By Using The Original Variables A & B.
A x C = 1.1111111111 ......
B x C = 0.9999999999 ......

B×C = 0.999... = B×A/B = A = 1
0.999.... = 1

proof discredited.

Anthony.R.Brown wrote:

The Variables below A & B are Both Single Start Values.
A = 1 "This has to be the Start Value for 1"
B = 0.9 "This has to be the Start Value for Infinite 0.9"
C = A / B = 1.1111111111......
A x C = 1.1111111111 ......"This is the same Calculation to Make a Number Infinite! as with B"
B x C = 0.9999999999 ......"This is now Infinite 0.9"

same as first one

Anthony.R.Brown wrote:

A starts as = 1
B starts as = 0.9
A x C results in a number > 1
B x C results in a number < 1
The point is A is 1
and B never = 1
If we are going to Infinitely multiply a number so that is becomes 1 "if possible"
Then a number that is already 1 must always be Greater!!

....also same as first one

Anthony.R.Brown wrote:

A starts as = 1
B starts as = 0.9
A x C results in a number > 1
B x C results in a number < 1
The point is A is 1
and B never = 1
If we are going to Infinitely multiply a number so that it becomes 1 "if possible"
Then a number that is already 1 must always be Greater

same as first one again

Anthony.R.Brown wrote:

A x C = 1.11111...
B x C = 0.99999....
It Only takes One Calculation for A x C to = 1.1111.....Because A is! and A eqauls 1
It takes B x C to = 0.9999999..... Which is One Calculation Because B is < 1 to start with!
If B was Now to Some how now Reach! or Equal 1 by Multiplication! this would only then = 1
This would be would still make B 0.1 < A because B never started as 1 or = 1 the same as A

same as first one again

Anthony.R.Brown wrote:

LET'S MAKE THIS AS CLEAR AS POSSIBLE! USING NEW VARIABLES.
N1 = 0.9 This is a Single Number Value
N2 = Infinite 0.9 This is an Infinite Number!
N3 = 1 This is a Single Number Value
N1..............( Here between N1 and N3 there are no other Numbers! Because N1 is the Single last Number!).............N3.
N2..............( Here between N2 and N3 there are an Infinite Amount of Numbers! Because N2 is an
Endless stream of Numbers!).............N3.

this just makes no sense, and is certainly not a proof

Anthony.R.Brown wrote:

If a Number has to be Infinitely Multiplied! To Try and Reach a Target Value! Then the Target Value! Must be Greater than the Number being Infinitely
Multiplied! Reason Being! If the Target Value was also Infinitely Multiplied! Then the Target Value would again be Greater!
Number Infinitely Multiplied! = 0.9 Target Value! = 1

same as previous.

Anthony.R.Brown wrote:

I would now like to Add another Variable to this Example! N4
This is for anyone who feels it's not possible to place another Number between N2 and N3.
N4 = The Maximum possible Number of .9's
Anyone who feels its not possible to place another Number between N2 and N3, all they have to do to prove how they feel! Is giving a Value for N4.
So now we have!.....
N2..............( Here between N2 and N3 there are an Infinite Amount of Numbers! Because N2 is an
Endless stream of Numbers!).............N3.
N2..............( How Ever! If..N4...is proved! Then the above is not True!).............N3.
N2..............( But as it Stands!..N4...Can have + .9's i.e More .9's Between! Because N2 is Infinite!).............N3.

same as previous.

Anthony.R.Brown wrote:

LET'S MAKE THIS EVEN MORE CLEARER!
N1 = 0.9 This is a Single Number Value
N2 = Infinite 0.9 This is an Infinite Number!
N3 = 1 This is a Single Number Value
N4 = The Maximum possible Number of .9's ?
N1..............( Here between N1 and N3 there are no other Numbers! Because N1 is the Last Single Number! Before ).............N3.
N2..............( Here between N2 and N3 there are an Infinite Amount of Numbers! Because N2 is an Endless stream of Numbers! Before ).............N3.
Below if Anyone can Give! and Prove! a Value for N4 Then the Above will be False! and not True! for then another .9 will not be able to be Inserted Between
N2..and..N3.
N2..............(.N4.)...........N3.

that certainly makes no sense

Anthony.R.Brown wrote:

N1 = 0.9 This is a Single Number Value And Yes! .9 is The Last Digit! Because its not an
Infinite Number the same as N2
N4 is the Variable to Represent the .9,s which is Between N2 and N3
Because N4 is an Infinite number then Any amount of .9,s can be Inserted to Represent N4
Unless! " Anyone can Give! and Prove! a Value

yadada yadada yadada still making no sense.

Anthony.R.Brown wrote:

N1 = 0.9 This is a Single Number Value
and is the last Single Value then 0.2,0.3,0.4,0.5,0.6,0.7,0.8, Then N1 and Then 1

what exactly does this have to do with the 'proof' of 0.999... <> 1?

Anthony.R.Brown wrote:

INFINITE 0.9 <> 1 PROOF By,Anthony.R.Brown,29/01/07.
The Variables below A1 & B1 are Both Single Start Values.
A1 = 1 "This has to be the Start Value for 1"
B1 = 0.9 "This has to be the Start Value for Infinite 0.9"
C = A1 / B1 = 1.1111111111...."There is only one Value & Variable for C"
A2 = A1 x C = 1.1111111111 ......"This is the same single Calculation as B2"
B2 = B1 x C = 0.9999999999 ......"This is now Infinite 0.9 and a single Calculation"
If B1 or B2 was at anytime to = A1 Then either would end up with the same Result as A2,but because it will take more than one single Calculation! for B1 or
B2 to = A1
Then its Impossible from the Start for Infinite 0.9 to ever = 1 in a single Calculation.

B2 = B1×C = B1×A1/B1 = A1 = 1
0.999... = 1

proof discredited

Anthony.R.Brown wrote:

( 1.1 ) x 0.9 = 0.99 " One Decimal Place = " 0.1 < 1
( 1.11 ) x 0.9 = 0.999 " Two Decimal Place's = " 0.1 < 1
( 1.111 ) x 0.9 = 0.9999 " Three Decimal Place's = " 0.1 < 1
( 1 / 0.9 ) x 0.9 = 0.9..... " Infinite Decimal Place's = " 0.1 < 1 "
The 0.1 Difference Above is Permanent! Because it is an Infinite Difference!!

(1/0.9)×0.9 = (1×0.9)/0.9 = 1
0.999... = 1

proof discredited

Anthony.R.Brown wrote:

To Back up my Proof above! I would like to Make an Immortal Quote:
" IF TWO NUMBERS START WITH A DIFFERENCE IN THEIR VALUES! AND BOTH ARE MULTIPLIED BY THE SAME AMOUNT! ONE VALUE WILL ALWAYS BE GREATER THAN THE OTHER!! "

what about 0?

any number multiplied by 0, gives 0.

Anthony.R.Brown wrote:

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 )

ah, finnaly something that can be argued about.

it is true, that for any finite lengthed digit composition, 0.9999, there will be a subsequent finite lengthed digit 0.0001.
however, you simply assume that it extends indefinately.

i.e. for any:

there is a number

such that they add to give 1.

however.

the complement to add to 1 would be

and 1/infinty is undefined, so such a number does not exist, therefore there does not exist a complement such that the number adds to give 1.
ofcourse, we can't add undefined to a number, so we use the value of its limit instead, that being

if this is so, then it means the number must already be 1, since the number that is needed to bring it to one... is 0

0.999... = 1

Anthony.R.Brown wrote:

I thought I made it Clear!
V1 = 0.99999999999999999999999999999999..Infinite.0.9...." = The 0.9 Value from the Start Onwards! "
V2 = 0.00000000000000000000000000000000..Infinite.0.1...." = The < 1 Value from the Start Onwards! "
V1 = Infinite 0.9
V2 = The Infinite Difference
No Matter how Long V1 is! V2 will always be the same Length!
Because V1 starts as 0.9 and Because V2 starts as 0.1 The Difference will always be the same!

same as above

Anthony.R.Brown wrote:

Below V1 = The Infinite 0.9 Sequence. : Below V2 = The < 1 Infinite Difference Sequence.
V1 = ( 0.9 ) + V2 = ( 0.1 ) = 1
V1 = ( 0.99 ) + V2 = ( 0.01 ) = 1
V1 = ( 0.999 ) + V2 = ( 0.001 ) = 1
V1 = ( 0.9999 ) + V2 = ( 0.0001 ) = 1
V1 = ( 0.99999 ) + V2 = ( 0.00001 ) = 1
V1 = ( 0.999999 ) + V2 = ( 0.000001 ) = 1
V1 = ( 0.9999999 ) + V2 = ( 0.0000001 ) = 1
V1 = ( 0.99999999 ) + V2 = ( 0.00000001 ) = 1
V1 = ( 0.999999999 ) + V2 = ( 0.000000001 ) = 1
V1 = ( 0.9999999999 ) + V2 = ( 0.0000000001 ) = 1
The Table above clearly shows no matter how long V1 is! it will always need the algebra + symbol for V1 to equal 1 ( V1 + V2 ) = 1
This proves Infinite 0.9 <> 1 because if ( V1 + V2 ) = 1 is allowed! it will be a contradiction to the term Infinite 0.9.

same as above

Anthony.R.Brown wrote:

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!!

same as above

Anthony.R.Brown wrote:

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 "

C = A/B×B = A = 1
0.999... = 1

D = A-C = A-A/B×B = A-A = 0

proof discredited.

Last edited by luca-deltodesco (2007-03-02 04:17:50)

MathsIsFun · 2007-03-02 10:27:29

Anthony.R.Brown wrote:

To keep everything Fare again! can all other Posts not to do with this Post! be removed again! including the Link above! to the other Post!

Fair means free of bias ... to remove posts with other viewpoints, including luca's detailed response above, would be bias, wouldn't it? And hence unfair, don't you agree?

So it is fair to allow discussion (but not abuse of course).

MathsIsFun · 2007-03-02 10:49:07

luca-deltodesco wrote:

and 1/infinty is undefined, so such a number does not exist, therefore there does not exist a complement such that the number adds to give 1.
ofcourse, we can't add undefined to a number, so we use the value of its limit instead, that being

I believe it is commonly accepted that 1/infinity = 0, due to that limit.

Sekky · 2007-03-02 13:35:05

MathsIsFun wrote:

I believe it is commonly accepted that 1/infinity = 0, due to that limit.

No, it isn't, it's indeterminate.

Last edited by Sekky (2007-03-02 13:35:22)

Ricky · 2007-03-02 14:10:36

Sekky wrote:

MathsIsFun wrote:
I believe it is commonly accepted that 1/infinity = 0, due to that limit.
No, it isn't, it's indeterminate.

I guess it all depends on what you mean by "1/infinity", since that doesn't make any sense.

But:

And so I guess in that sense, you would consider 1/infinity to be 0, as *any* function f that goes to infinity, 1/f goes to 0.

MathsIsFun · 2007-03-02 15:48:03

I will start a thread on 1/infinity: http://www.mathsisfun.com/forum/viewtopic.php?pid=61680

Could you please re-iterate your comments so I can deletw this side conversation

George,Y · 2007-03-02 16:06:32

luca, please tell me what's the infiniteth entry in your summation, literally what does ∞ mean?

You are not going to tell me it only means the summation goes on and on, are you?

If actually you cannot finish such summation, please do confess that you have defined the summation to be 1 rather than have got it (as Ricky has confessed earlier).

(Ricky you may be annoyed by the word "confess" but all your words are your confession unless you wrote that under mental disorder or you have corrected some previous words and stick to new words)

Anthony.R.Brown · 2007-03-03 00:41:23

Quote:

" C = A/B×B = A = 1
0.999... = 1
D = A-C = A-A/B×B = A-A = 0 "

A.R.B

C = ( A/B ) = ( Infinite 1.111...) x ( 0.9 ) = ( Infinite 0.999...)

0.999... <> 1 Because of an Infinite Difference of ( 0.001... )

D = 1 - ( Infinite 0.999...) = Infinite Difference of ( 0.001... )

proof credited.

Last edited by Anthony.R.Brown (Today.. )

Zhylliolom · 2007-03-03 04:43:10

Anthony.R.Brown wrote:

Quote:
" C = A/B×B = A = 1
0.999... = 1
D = A-C = A-A/B×B = A-A = 0 "
A.R.B
C = ( A/B ) = ( Infinite 1.111...) x ( 0.9 ) = ( Infinite 0.999...)
0.999... <> 1 Because of an Infinite Difference of ( 0.001... )
D = 1 - ( Infinite 0.999...) = Infinite Difference of ( 0.001... )

proof credited.
Last edited by Anthony.R.Brown (Today.. )

Using the assumption that 0.999... ≠ 1 to prove that 0.999... ≠ 1 is faulty logic... I'm sure you can realize the problem here without too much difficulty. The algebra which you have quoted is correct, why would A/B × B ≠ A? Please explain why this would happen. Until you can somehow convince everyone that basic algebra is incorrect, proof discredited.

George,Y · 2007-03-03 21:54:42

Zhylliolom wrote:

Using the assumption that 0.999... ≠ 1 to prove that 0.999... ≠ 1 is faulty logic...

So with the 0.999...=1 case...

Anthony.R.Brown · 2007-03-04 03:47:05

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

Anthony.R.Brown · 2007-03-06 01:47:53

To
Zhylliolom

Quote:

" why would A/B × B ≠ A? "

Because B is being Infinitely Multiplied by 1.1 which is .1 > 1

If the Number 1 was also Infinitely Multiplied by 1.1 it would again be greater than B

Thus Proving! a Number that starts with a Greater Value! and is Multiplied by the Same amount! will always be greater than another Number! that starts with a Lower Value!!

p.s Multiplying by Zero! is not possible!! because Zero! is not actually able to Multiply!!

Maelwys · 2007-03-06 02:02:04

Anthony.R.Brown wrote:

" why would A/B × B ≠ A? "
Because B is being Infinitely Multiplied by 1.1 which is .1 > 1
If the Number 1 was also Infinitely Multiplied by 1.1 it would again be greater than B

B isn't being infinitely multiplied by 1.1 as far as I can see... there's not even any infinitely recurring numbers in the formula, A = 1, B = 0.9, very straightforward. And using our definitions of multiplication and division, we know that the two are opposites and basically cancel each other out, so we know that A/B * B = A. Just like I have no idea what 5678544 / 23349 is, but I know that if I multiply the answer by 23349, I'm going to get a final answer of 5678544. I don't need a calculator to tell me that, pure logic will do it (and verifying it on a calculator I'm told that 5678544 / 23349 = 243.2028780675831941410767056405, and 243.2028780675831941410767056405 * 23349 = 5678544).

Anthony.R.Brown · 2007-03-06 02:09:18

To Maelwys

Quot: " B isn't being infinitely multiplied by 1.1 as far as I can see... "

A.RB

you always cant see very far!!

from my Formula

C ( A/B ) x B " Infinite 0.9 Value " ( = C ) using another variable! makes things clearer! it can also be wrote as " B is being infinitely multiplied by 1.1 "

Maelwys · 2007-03-06 02:17:30

Anthony.R.Brown wrote:

To Maelwys
Quot: " B isn't being infinitely multiplied by 1.1 as far as I can see... "
A.RB
you always cant see very far!!
from my Formula
C ( A/B ) x B " Infinite 0.9 Value " ( = C ) using another variable! makes things clearer! it can also be wrote as " B is being infinitely multiplied by 1.1 "

Sorry, I was looking at the wrong B. But you still didn't respond to the rest of the issue I had with your formula, just managed to pick up on the one inconsequential comment that I made and was wrong about.

Anthony.R.Brown · 2007-03-06 02:30:05

To Maelwys

I have answered you! just stick to what is in my Formula! and stop using other examples!

luca-deltodesco · 2007-03-06 02:50:29

and what is A/B×B, why, its equal to A

Anthony.R.Brown · 2007-03-06 02:53:47

To

luca-deltodesco

A.R.B

can you read?

Anthony.R.Brown · 2007-03-06 03:11:57

To

luca-deltodesco

A.R.B

" I thought not!!

A = 1

B = 0.9

A/B x B

1 / 0.9 = 1.111... x ( any Number you like! ) and it will always be 1.111... times the original Value! " Notice the Decimal point! it's very important!! "

luca-deltodesco · 2007-03-06 03:24:00

have you ever even studied basic algebra !?

A/B × B = A, for ALL B such that B =/= 0

look at it this way;

A/B is the same as A × 1/B, A multiplied by the multiplicative inverse of B.

the property of an inverse is that for ANY function f that has an inverse.

for example:

1/B, is the multiplicitve inverse of B, 1/B is the inverse operation of 1×B. following the law, 1/B×B = 1, and such A/B×B = A.

think of it logically, if you divide by a number, then multiply by the same number, nothing will change, same way that if you add a number, then subtract the same number, nothing will change, because negation is the additive inverse, subtraction is the inverse operation of addition.

Last edited by luca-deltodesco (2007-03-06 03:25:12)

Anthony.R.Brown · 2007-03-06 04:10:40

To luca-deltodesco

Quote:

" think of it logically, if you divide by a number, then multiply by the same number, nothing will change, "

A.R.B

Now that's what I was waiting for!!

1 is divided by 0.9 = 1.111....." this proves 0.9 is less than 1 "

i'm now going to mutiply it so nothing will change!

0.9 x 1.111.... " will always equal a Value less than 1 " because 0.9 was divided within a greater Value! that Value being 1

Math Is Fun Forum

#1 2007-02-15 02:44:46

INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

#2 2007-02-23 12:36:41

Re: INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

#3 2007-02-23 16:24:29

Re: INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

#4 2007-02-25 00:57:09

Re: INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

#5 2007-03-02 04:14:39

Re: INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

#6 2007-03-02 10:27:29

Re: INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

#7 2007-03-02 10:49:07

Re: INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

#8 2007-03-02 13:35:05

Re: INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

#9 2007-03-02 14:10:36

Re: INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

#10 2007-03-02 15:48:03

Re: INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

#11 2007-03-02 16:06:32

Re: INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

#12 2007-03-03 00:41:23

Re: INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

#13 2007-03-03 04:43:10

Re: INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

#14 2007-03-03 21:54:42

Re: INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

#15 2007-03-04 03:47:05

Re: INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

#16 2007-03-06 01:47:53

Re: INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

#17 2007-03-06 02:02:04

Re: INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

#18 2007-03-06 02:09:18

Re: INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

#19 2007-03-06 02:17:30

Re: INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

#20 2007-03-06 02:30:05

Re: INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

#21 2007-03-06 02:50:29

Re: INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

#22 2007-03-06 02:53:47

Re: INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

#23 2007-03-06 03:11:57

Re: INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

#24 2007-03-06 03:24:00

Re: INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

#25 2007-03-06 04:10:40

Re: INFINITE 0.9 <> 1 PROOF : COMPLETE : By,Anthony.R.Brown,15/02/07

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