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

Anthony.R.Brown · 2007-02-02 00:56:34

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

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( 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!!

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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!! "

luca-deltodesco · 2007-02-02 05:23:26

what exactly, are you saying with the 0.1, it makes no sense, we know 0.1 < 1, what does this have to do with anything else your saying, if you are meant to be infering the difference between the value and 1. then it would be like this (modifying your post in bold)

( 1.1 ) x 0.9 = 0.99 " One Decimal Place = " 0.01 > 0

( 1.11 ) x 0.9 = 0.999 " Two Decimal Place's = " 0.001 > 0

( 1.111 ) x 0.9 = 0.9999 " Three Decimal Place's = " 0.0001 > 0

( 1 / 0.9 ) x 0.9 = 0.9..... " Infinite Decimal Place's = " 0.000000......1 > 0, 0 = 0

now, the problem here, is there is no such thing as 0.0000......1 it makes no sense, what the 'number' would be, is an infinite amount of zero's, followed by a 1, but how can you put something after something that is endless, surely you can see, that such would be to define an end to the number of zeros for which to put the one after, but infinty means endless, so there is no such end for which to put the number one, so it can be concluded that 0.00000.....1 = 0

also, by rearrangement of ( 1 / 0.9 ) x 0.9 we have this:

( 1 / 0.9 ) x 0.9 = 0.9.....

by rules of multiplication,

therefore, you have also concluded that 0.999.... = 1

Last edited by luca-deltodesco (2007-02-02 05:28:43)

George,Y · 2007-02-02 21:34:34

but how can you put something after something that is endless, surely you can see, that such would be to define an end to the number of zeros for which to put the one after, but infinty means endless
-how can you reach endless? Or how can you produce endless?

luca-deltodesco · 2007-02-02 21:51:07

you cant reach endless, thats the whole point of what im saying.

why do you need to produce it? what exactly are you trying to get at here.

George,Y · 2007-02-02 23:42:34

But 1 is reachable, not endless. At least from the ancient, classic defination.

George,Y · 2007-02-02 23:45:54

I mean 1 apple, that is 1, not 2, not made up of 9/10+9/100+9/1000+...endless.
I eat it as a whole-It's over.
But if it is made up of infinite parts, forever growing parts, I wonder how I can eat it- no, them.

kylekatarn · 2007-02-03 00:20:49

George,Y wrote:

how can you reach endless? Or how can you produce endless?

You can "reach the unreachable" with Limits from good old friend Calculus, and that's all we need to understand that 0.(9) = 1 or some other anti-common-sense equality. "reach" in the sense of "getting really close to".

Anthony.R.Brown wrote:

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

0.(9) "doesn't exist on the paper", only on our minds because it is a limit. A limit of something. An infinite sum's limit of very small things like 0.009, 0.000009, 0.0000000000000000000009... and it gets smaller as we add up terms. So you can't write it down with a pen, because there is always another term. In the paper, you never reach 0.(9).

it is true that 0.9 <> 1
and 0.99 <> 1
and 0.999 <> 1
and ...etc

but this way you never, never, ever reach 0.(9) = 0.999999999..(inf. # of 9's)

To build the "numeric amount" 0.(9) you need and infinite sum, Limits are implicit here, because you can only know "what are we getting close to" when adding 0.9+0.09+0.009+(...). When you write 0.9+0.09+0.009+... on a paper you are implicitly summing and infinite number of terms, and limits are involved again, even if you don't notice them.

When we mess around with infinity strange things happen, like 0.(9) = 1, lengths become areas, areas become volumes, mass densities becomes masses.. and we enter the mighty world of infinitesimal calculus ^^

It's natural, we sometimes want to explore things our way and create our rules. But later we understand that our efforts were an attempt to reinvent something that already was well-studied and properly defined.

Anthony.R.Brown · 2007-02-03 01:32:08

Now! I see everyone is starting to understand what I and others have been saying!

" 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!! "

A.R.B

Anthony.R.Brown · 2007-02-03 01:42:13

To kylekatarn

Quote:

"butt his way you never, never, ever reach 0.(9) = 0.999999999..(inf. # of 9's)"

A.R.B

We don't need to try and reach an end! we have the Number 1 for That!

I am quite happy to know there is a Number Infinitely smaller than 1

kylekatarn · 2007-02-03 01:59:50

Anthony.R.Brown wrote:

Now! I see everyone is starting to understand what I and others have been saying!
" 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!! "
A.R.B

let x, y, Δ ∈ R so that y = x + Δ, Δ>0

x < x + Δ
x < y

now let k ∈ R.

case k<0:

x < y
k x > k y
k x > k x + k Δ
0 > k Δ => Δ > 0 True

case k > 0:

x < y
k x < k y
k x < k x + k Δ
0 < k Δ => Δ > 0 True

case k = 0

x < y
0 x = 0 = 0 y

Yes, this is true, except the trivial case, k=0.

kylekatarn · 2007-02-03 02:11:10

Anthony.R.Brown wrote:

We don't need to try and reach an end! we have the Number 1 for That!

Defining precise concepts is important, so why don't you write a paper on this subject, a well structured document with your ideas, theorems, proofs and beliefs?

But if you want to label it "Mathematics" it must be consistent with existing axioms, theorems, lemmas, etc. Anyway, I would like to see your theory in a formal way so we can discuss what you say with correctness and logical basis.

krassi_holmz · 2007-02-03 11:59:22

Again the old story!
Anthony, just try to beleive all the people telling you that
0.999... = 1!

krassi_holmz · 2007-02-03 12:05:12

And yep, we've got 14 more (or maybe a lot more) pages on this theme:
http://www.mathsisfun.com/forum/viewtopic.php?id=658

Anthony.R.Brown · 2007-02-05 02:22:52

INFINITE 0.9 <> 1 PROOF : CONCLUSION By,Anthony.R.Brown,06/02/07.
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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 )

kylekatarn · 2007-02-05 02:58:11

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 )

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.

Last edited by kylekatarn (2007-02-05 03:18:04)

Patrick · 2007-02-05 02:59:25

What are you talking about, seriously?

That's okay, but the next, is it supposed to mean

Maelwys · 2007-02-05 04:58:08

Anthony.R.Brown wrote:

V1 = 0.9999999999...." = The 0.9 Value from the Start Onwards! "
V2 = 0.0000000001...." = The < 1 Value from the Start Onwards! "

V2 can be read 3 different ways, and unfortunately none of them make sense.
V2 = 0.00000000010000000000100000000001... (repeating the entire sequence to infinitely, which just makes for a really odd number when added to V1)
V2 = 0.00000000011111111111111111111111... (repeating the final digit to infinitely, which makes a different, equally odd number when added to V2)
Or, I assume that by your definition for V2 you mean to say
V2 = 0.00000000...1 (ie: an infinitely long string of zeros with a one on the end). In this case you have to consider as already mentioned above several times, that there is NO end to an infinitely long string of zeros, so there is nowhere to put that one, so it essentially doesn't exist. Because if there's room to stick a one on the "end" of the string of zeros, then that means it's not infinitely long yet and you have to put another zero there instead... and if you're able to put the one after that zero, then instead you have to put another zero there first (and so on and so on and so on). So that theory doesn't work either, sorry.

MathsIsFun · 2007-02-05 08:41:10

Exactly Maelwys (and Welcome to the Forum!), "infinite" says "no end".

George,Y · 2007-02-05 13:16:24

Does "no end" mean "growing forever"?

luca-deltodesco · 2007-02-05 18:44:09

no, no end, means simply that, there is no growing.. where exactly are you getting the conotation of growing from?

Ricky · 2007-02-05 18:59:59

Growing tends to imply that a number is moving it's position on the real line.

Dross · 2007-02-06 00:26:42

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.

Anthony.R.Brown · 2007-02-06 01:02:20

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!

Toast · 2007-02-06 01:07:51

Why don't we just forfeit... it would be so much easier...

Maelwys · 2007-02-06 01:43:22

MathsIsFun wrote:

Exactly Maelwys (and Welcome to the Forum!), "infinite" says "no end".

Thanks for the welcome. If it's any consolation, some good has come of this conversation... I was led to these forums by a link that Anthony posted on Wikipedia (trying to cite his post on these forums as proof that his theory was true, to get me to create a page on Wikipedia explaining his theory). ;-) That's also why a lot of his arguments seem generic and never seem to directly answer any of the questions/challenges people post for him, because he's carrying on the same arguments both here and on Wikipedia.

Anyway, to Anthony: (copied from my reply to the same argument you just made on Wiki):
Sorry, there's still a couple problems with this. The main one is your definition of V2. You can't have a number that contains and infinite number of 0s, followed by a 1. Infinite means "never ending". That means that as long as you can put another number at the "end" of the string of numbers, it MUST be another zero (to fulfill the "never ending string" definition. So you can't possibly put a one at the "end" of the string, since there is no end. It seems that basically, your entire problem with accepting the proofs presented here is with understanding the definition of infinite. Infinite isn't a "really big" number. It's a limitlessly big number. So an infinite number of zeros doesn't mean that you just keep writing zeros for a long time and then eventually stop and put a 1 on the end. It means that you keep writing zeros forever. Forever and ever. You'll never be able to put a one anywhere. Therefor, there is no possible number that could be added to 0.999... to give 1. And THAT, is why 0.999... equals 1, because if there's no possible number that you could add to it to achieve 1, then there's no difference between the two, which means that they're the same number.

Math Is Fun Forum

#76 2007-02-02 00:56:34

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

#77 2007-02-02 05:23:26

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

#78 2007-02-02 21:34:34

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

#79 2007-02-02 21:51:07

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

#80 2007-02-02 23:42:34

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

#81 2007-02-02 23:45:54

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

#82 2007-02-03 00:20:49

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

#83 2007-02-03 01:32:08

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

#84 2007-02-03 01:42:13

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

#85 2007-02-03 01:59:50

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

#86 2007-02-03 02:11:10

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

#87 2007-02-03 11:59:22

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

#88 2007-02-03 12:05:12

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

#89 2007-02-05 02:22:52

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

#90 2007-02-05 02:58:11

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

#91 2007-02-05 02:59:25

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

#92 2007-02-05 04:58:08

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

#93 2007-02-05 08:41:10

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

#94 2007-02-05 13:16:24

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

#95 2007-02-05 18:44:09

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

#96 2007-02-05 18:59:59

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

#97 2007-02-06 00:26:42

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

#98 2007-02-06 01:02:20

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

#99 2007-02-06 01:07:51

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

#100 2007-02-06 01:43:22

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

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