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## #76 2006-10-11 08:19:02

Ricky
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### Re: I disagree with 0.999... = 1

Yes Kurre, that is why we typically restrict infinity from being a number.  There are also many different types of infinity, and some infinities are larger than others.

"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..."

## #77 2006-10-19 21:32:11

gudipudi
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### Re: I disagree with 0.999... = 1

yeah sounds tricky

## #78 2006-11-16 23:25:11

Anthony.R.Brown
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### Re: I disagree with 0.999... = 1

Its impossible for Infinite 0.9 to ever = 1

Beacause there will always be a difference of Infinite 0.1

A.R.B

## #79 2006-11-17 06:16:20

Ricky
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### Re: I disagree with 0.999... = 1

Its impossible for Infinite 0.9 to ever = 1

Beacause there will always be a difference of Infinite 0.1

If such infinities exist in your number system, you are right.

However, the real numbers are defined to not contain such "Infinite 0.1" and thus, we must replace this with 0, making them equal.

"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..."

## #80 2006-11-17 23:00:30

Anthony.R.Brown
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### Re: I disagree with 0.999... = 1

In the Real World I have tried to find the end of the Universe! but its just not there!
As a human I will not accept  there is an End! when I see the so called end of an Infinite Number,by the Magic of Infinite 0.999999999999......becoming 1?
I will know behind this there will always be more .999999999999999999's for Ever!

## #81 2006-11-18 05:57:32

Dross
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### Re: I disagree with 0.999... = 1

#### Anthony.R.Brown wrote:

In the Real World I have tried to find the end of the Universe! but its just not there!
As a human I will not accept  there is an End! when I see the so called end of an Infinite Number,by the Magic of Infinite 0.999999999999......becoming 1?
I will know behind this there will always be more .999999999999999999's for Ever!

Yes... there are an infinite number of "9"s in 0.999...(recurring) - that's why it equals one!

You as a human will not be able to add an infinite number of "9"s together - but numbers are not restricted by time, space and the physical laws that we are. You can think of all the "9"s being added together "at the same time" (as it were) - not one after the other.

Bad speling makes me [sic]

## #82 2006-11-18 07:16:57

Ricky
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### Re: I disagree with 0.999... = 1

In the Real World I have tried to find the end of the Universe! but its just not there!
As a human I will not accept  there is an End! when I see the so called end of an Infinite Number,by the Magic of Infinite 0.999999999999......becoming 1?
I will know behind this there will always be more .999999999999999999's for Ever!

You misunderstand.

You talk about the number Infinite 0.1.  It takes advanced courses in math to understand this, but such a number does not exist in the real numbers.  And that's a good thing too.  If such a number did exist, we would lose almost all of calculus such as limits, derivatives, and integrals.

But the number infinite 0.1, not matter what way you wish to say it, does not exist in the real numbers.  The real numbers are defined in such a way to ensure that such a number does not exist.

However, if you go to other number systems such as the surreals and hyperreals, "infinite 0.1" (written is a more mathematical form) does in fact exist, and it is true that 0.999... does not equal 1.  But again, this is in a different number system.  Typically when numbers are talked about, we talk about them within the real numbers.

"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..."

## #83 2006-11-19 00:27:47

Anthony.R.Brown
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### Re: I disagree with 0.999... = 1

Infinite 0.9 starts as 0.9 (stage one)

then Infinite 0.99  (stage two)

then Infinite 0.999  (stage three) etc.....................................

1 subtract 0.9 (stage one) = 0.1 this number is Infinite because it is a continuous difference!

so Infinite    0.9999999999999999999999999999999999.......

has Infinite  0.1111111111111111111111111111111111.......

running along side Infinite 0.9 for ever! the two numbers are never add together!

Resulting in an eternal difference of Infinite 0.1...................................................

A.R.B

## #84 2006-11-19 02:17:27

Ricky
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### Re: I disagree with 0.999... = 1

Uhh....

0.9999999999999999
+0.1111111111111111
---------------------------
1.111111111111111111

Thus, 1 - 0.9999999999999 does not equal 0.11111111....

"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..."

## #85 2006-11-19 03:48:37

Dross
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### Re: I disagree with 0.999... = 1

#### Anthony.R.Brown wrote:

Infinite 0.9 starts as 0.9 (stage one)

then Infinite 0.99  (stage two)

then Infinite 0.999  (stage three) etc.....................................

1 subtract 0.9 (stage one) = 0.1 this number is Infinite because it is a continuous difference!

so Infinite    0.9999999999999999999999999999999999.......

has Infinite  0.1111111111111111111111111111111111.......

running along side Infinite 0.9 for ever! the two numbers are never add together!

Resulting in an eternal difference of Infinite 0.1...................................................

A.R.B

Anthony - you are beginning to seem very much like George from the other thread. I have said before:

#### Dross wrote:

You as a human will not be able to add an infinite number of "9"s together - but numbers are not restricted by time, space and the physical laws that we are. You can think of all the "9"s being added together "at the same time" (as it were) - not one after the other.

And you just go ahead and ignore me - and Ricky, who also has tried to correct your logic. Was there any point to us writing our poss? Was there any point in you writing your original post? Not if you're just going to ignore all replies to your posts whilst reluctantly repeating things that we have told you are misunderstandings.

Don't get me wrong - I don't think I'm right all the time. But if you see me post something and you think that I am wrong, please address it, as opposed to ignoring it as you and George have been doing.

Once again, the major error in your post (quoted above) is that you are trying to add digits sequentially, one at a time. Of course you're never going to reach one if you do it like that! There's no way that you, as a human, can do that. But what you are doing above is adding together a growing, finite number of digits, which will not behave at all like the constant, infinite number of digits you're trying to approximate.

Bare in mind that by adding a finite number of digits to the end of 0.99, you are no closer to having an infinite number of digits - you're still "infinitely far away", as it were.

Also bare in mind that the "number" is not restricted by time and space the same way you are - it doesn't have to pick up a pencil and start writing down the summation of numbers, which of course a human would never be able to complete. You can think of all the digits being, as I have said before, "added at the same time".

Last edited by Dross (2006-11-19 03:50:52)

Bad speling makes me [sic]

## #86 2006-11-21 01:27:43

Anthony.R.Brown
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### Re: I disagree with 0.999... = 1

So here is the Challenge!

Can anyone prove Infinite 0.9 = 1

The proof someone puts forward must be shown as a Mathematical Proof.
I can Prove Infinite 0.9 (Stage one) Starts with 0.9 which is less than 1 to Start with.
So for me to be proved wrong someone has to show the Mathematics on how to Bridge the Gap from 0.9 to 1.

This is all someone has to do?   Infinite 0.9 ( Bridge this Gap with Math Please! )  1

A.R.B

## #87 2006-11-21 10:05:04

Ricky
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### Re: I disagree with 0.999... = 1

To avoid multiple posts, this topic is being locked.

For further discussion, please post in the topic here

"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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