# .99999 does not equal 1

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#### WardoggKC130FE

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##### Re: .99999 does not equal 1
« Reply #690 on: September 12, 2008, 08:07:03 AM »
There is a distance of 8 feet.  And to cover that distance an object traveled half its distance remaining to the destination in one jump.  IE jumps 4ft then 2ft then 1 ft then .5ft... when would that object finally reach its destination?

#### Jack

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##### Re: .99999 does not equal 1
« Reply #691 on: September 12, 2008, 08:09:50 AM »
That's a finite range with an infinite number of scenarios through division. We are talking about infinite range.

Oh, and you ignored this part,
It goes on forever without stopping.
Thus, you can correct your mistake here,

.999.... does not equal 1 there is ALWAYS one more 9.

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#### Dr Matrix

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##### Re: .99999 does not equal 1
« Reply #692 on: September 12, 2008, 08:10:55 AM »
Assuming a constant rate of jumping, never.

You're aware that the same arguments can be used to allow fractal shapes to have a finite area but infinite perimeter, right? Infinite series allow all sorts of weird things to happen, but that doesn't make them untrue.
Quote from: Arthur Schopenhauer
All truth passes through three stages. First, it is ridiculed. Second, it is violently opposed. Third, it is accepted as being self-evident.

#### WardoggKC130FE

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##### Re: .99999 does not equal 1
« Reply #693 on: September 12, 2008, 08:13:10 AM »
That's a finite range with an infinite number of scenarios through division. We are talking about infinite range.

Oh, and you ignored this part,

NO we are not talking about an infinite range.  1.0 is not infinite and by putting a bunch of 9s behind a decimal point trying to reach 1.0 is the same thing as my scenario i just posted.  I didn't ignore it.  There was nothing to be corrected.

#### Jack

• 5179
##### Re: .99999 does not equal 1
« Reply #694 on: September 12, 2008, 08:18:14 AM »
NO we are not talking about an infinite range.
Yes, we are.

1.0 is not infinite and by putting a bunch of 9s behind a decimal point trying to reach 1.0 is the same thing as my scenario i just posted.
How much is "a bunch"?

I didn't ignore it.  There was nothing to be corrected.
Yes, you did. The correction is: there will never be an end. Your "always one more 9" assumes there is an end.

#### WardoggKC130FE

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##### Re: .99999 does not equal 1
« Reply #695 on: September 12, 2008, 08:20:50 AM »
NO we are not talking about an infinite range.
Yes, we are.

1.0 is not infinite and by putting a bunch of 9s behind a decimal point trying to reach 1.0 is the same thing as my scenario i just posted.
How much is "a bunch"?

I didn't ignore it.  There was nothing to be corrected.
Yes, you did. The correction is: there will never be an end. Your "always one more 9" assumes there is an end.

No we are not.  1.0 is not infinite

Bunch = infinite

What does always mean?  If there will always be one more that would suggest, never ending, IE infinite.

#### Jack

• 5179
##### Re: .99999 does not equal 1
« Reply #696 on: September 12, 2008, 08:33:33 AM »
No we are not.  1.0 is not infinite
No, we are saying 0.(9).

Bunch = infinite
Thus, the error between 0.999... and 1 is infinitely small.

0.(9) = 1

What does always mean?  If there will always be one more that would suggest, never ending, IE infinite.
Then word your sentence better next time. As I've said in my previous post, I assumed your "always one more 9" meant there will always be a 9 in the end. It should be "there is an infinite number of 9s after 0.9".

#### WardoggKC130FE

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##### Re: .99999 does not equal 1
« Reply #697 on: September 12, 2008, 08:38:44 AM »
That's a finite range with an infinite number of scenarios through division. We are talking about infinite range.

Speaking of ignoring you forgot to answer my question.

Here let me put it a different way.

An object has a distance of 1ftto a destination.  The object covers that distance by jumping .9ft then .09ft then .009ft...always adding another 0 and 9 to that when does it reach the destination?
« Last Edit: September 12, 2008, 08:41:55 AM by WardoggKC130FE »

#### Jack

• 5179
##### Re: .99999 does not equal 1
« Reply #698 on: September 12, 2008, 08:46:46 AM »
That's a finite range with an infinite number of scenarios through division. We are talking about infinite range.

Speaking of ignoring you forgot to answer my question.

Here let me put it a different way.

An object has a distance of 1ftto a destination.  The object covers that distance by jumping .9ft then .09ft then .009ft...always adding another 0 and 9 to that when does it reach the destination?

#### WardoggKC130FE

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##### Re: .99999 does not equal 1
« Reply #699 on: September 12, 2008, 08:50:23 AM »

#### Jack

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##### Re: .99999 does not equal 1
« Reply #700 on: September 12, 2008, 08:58:36 AM »
Was my quote too hard for your to understand?

Please do not ignore the bold part.
That's a finite range with an infinite number of scenarios through division. We are talking about infinite range.

You whole point is that there is this little finite 1 and it takes infinite 9s after 0.9 to reach it, thus 0.(9) != 1. That is wrong, because, which you also ignored, the error between 0.(9) and 1 is infinitely small; this way, we can't measure it, so it is neglected.

#### WardoggKC130FE

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##### Re: .99999 does not equal 1
« Reply #701 on: September 12, 2008, 09:09:34 AM »
You whole point is that there is this little finite 1 and it takes infinite 9s after 0.9 to reach it, thus 0.(9) != 1. That is wrong, because, which you also ignored, the error between 0.(9) and 1 is infinitely small; this way, we can't measure it, so it is neglected.

Oh now I get it.  Because you can't measure it, it is insignificant and has to be thrown out. The fact that you say there is an error proves, regardless of its size, .999... does not equal 1.0.

#### Jack

• 5179
##### Re: .99999 does not equal 1
« Reply #702 on: September 12, 2008, 09:17:36 AM »
Because you can't measure it, it is insignificant and has to be thrown out. The fact that you say there is an error proves, regardless of its size, .999... does not equal 1.0.
If you can measure it, then prove to the world 0.(9) != 1.

#### WardoggKC130FE

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##### Re: .99999 does not equal 1
« Reply #703 on: September 12, 2008, 09:22:58 AM »
Because you can't measure it, it is insignificant and has to be thrown out. The fact that you say there is an error proves, regardless of its size, .999... does not equal 1.0.
If you can measure it, then prove to the world 0.(9) != 1.

You just proved it.  There is an error.  Infinitely small.

#### Jack

• 5179
##### Re: .99999 does not equal 1
« Reply #704 on: September 12, 2008, 09:25:47 AM »
0.(9) = 1 because the error cannot be measured. Do I have to make it simpler?

#### WardoggKC130FE

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##### Re: .99999 does not equal 1
« Reply #705 on: September 12, 2008, 10:01:06 AM »
0.(9) = 1 because the error cannot be measured. Do I have to make it simpler?

There is an error.
« Last Edit: September 12, 2008, 10:07:00 AM by WardoggKC130FE »

#### Jack

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##### Re: .99999 does not equal 1
« Reply #706 on: September 12, 2008, 10:19:06 AM »

#### WardoggKC130FE

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##### Re: .99999 does not equal 1
« Reply #707 on: September 12, 2008, 12:44:53 PM »
It still exists.

#### cmdshft

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##### Re: .99999 does not equal 1
« Reply #708 on: September 12, 2008, 12:46:59 PM »
3/3 = 1

1/3= .33333...

Therefore, (.33333333....) + (.33333333....) + (.33333333....) = (.99999999...) = 1

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#### Mrs. Peach

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##### Re: .99999 does not equal 1
« Reply #709 on: September 12, 2008, 12:53:04 PM »
3/3 = 1

1/3= .33333...

Therefore, (.33333333....) + (.33333333....) + (.33333333....) = (.99999999...) = 1

This remains the best demonstration of the problem in the whole 37 page thread.

Another win for Hara!

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#### Percy

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##### Re: .99999 does not equal 1
« Reply #710 on: September 12, 2008, 01:42:56 PM »
Hello people, heres my worthless two cents.

1 does IN FACT = 0.9 (recurring).

BUT

1/3 does NOT = 0.3 (recurring)
I'm sorry, It just doesn't. Go read a further maths text book.

ACTUAL PROOF would be something like this:

-------------------------------------
lets say x=0.9 recurring.

therefore 10x = 9.9 recurring.

and if we do 10x - x = 9,
therefore x = 1
-------------------------------------

There is absolutely no flaw in that.

Look pal i'm english, we invented the language so dont tell me when im getting it wrong.

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#### Mrs. Peach

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##### Re: .99999 does not equal 1
« Reply #711 on: September 12, 2008, 01:46:55 PM »
The Percy solution lacks elegance.

#### cmdshft

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##### Re: .99999 does not equal 1
« Reply #712 on: September 12, 2008, 02:07:33 PM »
3/3 = 1

1/3= .33333...

Therefore, (.33333333....) + (.33333333....) + (.33333333....) = (.99999999...) = 1

This remains the best demonstration of the problem in the whole 37 page thread.

Another win for Hara!

Wheeee!

#### Parsifal

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##### Re: .99999 does not equal 1
« Reply #713 on: September 12, 2008, 05:19:32 PM »
My solution is still the best one.

Take An to be the nth element in the sequence 9 * 10-1 + 9 * 10-2 + ... + 9 * 10-n, where n is a finite positive integer.

Then there is some number B such that An < B < 1.

But because limn→∞ An = 1, then there will be some finite positive integer k such that An+k > B.

Therefore, every number that is less than 1 can be exceeded by An simply by making n a large enough, but finite, positive integer.

Since to have an infinite number of 9s simply means that no matter how large the number of finite 9s you count, there will always be at least one more, 0.999... = 1.

QED

Also, Wardogg, if 0.(9) != 1, then what is a number between 0.(9) and 1?
I'm going to side with the white supremacists.

#### WardoggKC130FE

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##### Re: .99999 does not equal 1
« Reply #714 on: September 12, 2008, 06:56:54 PM »
My solution is still the best one.

Take An to be the nth element in the sequence 9 * 10-1 + 9 * 10-2 + ... + 9 * 10-n, where n is a finite positive integer.

Then there is some number B such that An < B < 1.

But because limn→∞ An = 1, then there will be some finite positive integer k such that An+k > B.

Therefore, every number that is less than 1 can be exceeded by An simply by making n a large enough, but finite, positive integer.

Since to have an infinite number of 9s simply means that no matter how large the number of finite 9s you count, there will always be at least one more, 0.999... = 1.

QED

Also, Wardogg, if 0.(9) != 1, then what is a number between 0.(9) and 1?

0.999....

#### Parsifal

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##### Re: .99999 does not equal 1
« Reply #715 on: September 12, 2008, 07:20:04 PM »
0.999....

0.(9) is a different notation for 0.999... . They mean the same thing. Again, what is a number between 0.(9) and 1, or between 0.999... and 1, if you will?
I'm going to side with the white supremacists.

#### WardoggKC130FE

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##### Re: .99999 does not equal 1
« Reply #716 on: September 12, 2008, 07:25:09 PM »
0.999....

0.(9) is a different notation for 0.999... . They mean the same thing. Again, what is a number between 0.(9) and 1, or between 0.999... and 1, if you will?

It's a nonsense question.  You admit that if there was a finite number of 9s after the decimal then it wouldn't equal 1.0 no matter HOW many 9s where after that decimal, yet then you say that .999... equals 1.0.  You can have the cake and eat it too.  If it doesn't matter how many 9s I have after the decimal then it doesn't matter if I say it's an infinite amount.

#### cmdshft

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##### Re: .99999 does not equal 1
« Reply #717 on: September 12, 2008, 07:29:27 PM »
And since you cannot add onto an infinitely long number another digit (that's the definition of infinite), there is no number you can put between 0.(9) and 1, so the two are mutually inclusive. 0.(9)=1.

#### Parsifal

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##### Re: .99999 does not equal 1
« Reply #718 on: September 12, 2008, 07:50:22 PM »
It's a nonsense question.  You admit that if there was a finite number of 9s after the decimal then it wouldn't equal 1.0 no matter HOW many 9s where after that decimal, yet then you say that .999... equals 1.0.  You can have the cake and eat it too.  If it doesn't matter how many 9s I have after the decimal then it doesn't matter if I say it's an infinite amount.

0.999... does not fit into the category of numbers with a finite number of 9s after the decimal point.
I'm going to side with the white supremacists.