# .99999 does not equal 1

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#### Oscar Wilde

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##### Re: .99999 does not equal 1
« Reply #30 on: August 09, 2008, 10:41:23 PM »

#### Parsifal

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##### Re: .99999 does not equal 1
« Reply #31 on: August 09, 2008, 10:46:48 PM »
I'm going to side with the white supremacists.

#### narcberry

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##### Re: .99999 does not equal 1
« Reply #32 on: August 09, 2008, 10:48:46 PM »
You don't need to put 3s forever.  That's what the ellipses represent.  Or putting a line over the number, if you prefer.  But it's a fact that .333..., if you understand the ellipses to represent an infinite number of 3s, is equal to 1/3.  And .999... is equal to 1.

The point is you can't write 3's forever, because it's impossible. That's why .999 can never equal 1, because you can't ever write that many nines!

#### General Douchebag

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##### Re: .99999 does not equal 1
« Reply #33 on: August 10, 2008, 02:26:20 AM »
You could put something on the key...
No but I'm guess your what? 90? Cause you just so darn mature </sarcasm>

#### Raist

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##### Re: .99999 does not equal 1
« Reply #34 on: August 10, 2008, 07:32:31 AM »
I just don't understand what your equation, and your subsequent explaination of asymptotes has to do with jdoe's proof. What did you  clarify for people? Please explain yourself.

Is this your clumsy way of explaining that the limit of (1/10^x) is 0 as x approaches infinity?
what does a limit find; an answer or an approximate value?

The limit gives an exact a sum to an infinite series  (the sum is 1).  Since when the hell is a limit ever an approximation? I think the definition of a limit is obvious to anyone who has ever had a class dealing with them (a calculus class), and you are no substitute for a textbook to those who have not.
lolwut?

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#### Bushido

##### Re: .99999 does not equal 1
« Reply #35 on: August 10, 2008, 07:58:50 AM »
narc is right

0.99...9 < 1 for any fixed number n of 9s beyond the decimal point. Furthermore, 0.99...99 > 0.99...9.
\--|--/                                                                                                        \--|---/    \--|--/
|                                                                                                                |             |
n 9s                                                                                                         (n+1) 9s       n 9s

Thus, the sequence {0.99...9} is a monotonicaly increasing and bounded. According to a famous theorem from calculus, it is convergent, meaning it has a unique limit. Let us denote this limit as x. Then we have:

x = 0.99...         (notice that the sequence of 9s goes to infinity now)
Multyplying by 10, we get:
10x = 9.99...
Subtracting these two expressions and we have:
10x - x = 9.99... - 0.99...

9x = 9

x - 9/9

x = 1

So, the limit is 1, indicating that, when the number of decimals goes to infinity 0.99... = 1.

However, narc is wrong in saying that when a number has infinite number of decimal places, it does not exist. All irrational numbers (like √2 or π) have a decimal representation with infinite number of non-repeating decimals. However, they do exist and are used in mathematics all the time.
« Last Edit: August 10, 2008, 08:00:43 AM by Bushido »

#### Raist

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##### Re: .99999 does not equal 1
« Reply #36 on: August 10, 2008, 08:02:50 AM »
I love on the old thread where the math "major" found the limit to it and said that indicated that it equals one. I left the thread.

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#### cbarnett97

• 2746
##### Re: .99999 does not equal 1
« Reply #37 on: August 10, 2008, 12:04:07 PM »
narc is right

0.99...9 < 1 for any fixed number n of 9s beyond the decimal point. Furthermore, 0.99...99 > 0.99...9.
\--|--/                                                                                                        \--|---/    \--|--/
|                                                                                                                |             |
n 9s                                                                                                         (n+1) 9s       n 9s

Thus, the sequence {0.99...9} is a monotonicaly increasing and bounded. According to a famous theorem from calculus, it is convergent, meaning it has a unique limit. Let us denote this limit as x. Then we have:

x = 0.99...         (notice that the sequence of 9s goes to infinity now)
Multyplying by 10, we get:
10x = 9.99...
Subtracting these two expressions and we have:
10x - x = 9.99... - 0.99...

9x = 9

x - 9/9

x = 1

So, the limit is 1, indicating that, when the number of decimals goes to infinity 0.99... appraoches1.

However, narc is wrong in saying that when a number has infinite number of decimal places, it does not exist. All irrational numbers (like √2 or π) have a decimal representation with infinite number of non-repeating decimals. However, they do exist and are used in mathematics all the time.
Fixed
« Last Edit: August 10, 2008, 12:06:43 PM by cbarnett97 »
Only 2 things are infinite the universe and human stupidity, but I am not sure about the former.

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#### Nightmare

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##### Re: .99999 does not equal 1
« Reply #38 on: August 10, 2008, 12:05:28 PM »
Does a circle exist?
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#### sokarul

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##### Re: .99999 does not equal 1
« Reply #39 on: August 10, 2008, 12:07:54 PM »
3/3 = 1

1/3= .33333...

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

.3333 repeating is not a full 1/3.
ANNIHILATOR OF  SHIFTER

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#### cbarnett97

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##### Re: .99999 does not equal 1
« Reply #40 on: August 10, 2008, 12:08:39 PM »
Does a circle exist?
why wouldnt it?
Only 2 things are infinite the universe and human stupidity, but I am not sure about the former.

#### Roundy the Truthinessist

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##### Re: .99999 does not equal 1
« Reply #41 on: August 10, 2008, 12:13:34 PM »
Do repeating decimals as they are written using standard notation (ellipses, or lines or dots above the repeating digits) no longer validly represent fractions?

Of course it's true that .99999 does not equal 1.  There's no finite number of 9s that can be written in there that will ever make it equal 1.  But if you understand that .999... represents a decimal point followed by an infinite number of 9s, then .999... is equal to 1, plain and simple.

Unless repeating decimals are no longer valid ways to represent fractions.  But if that's the case, Wikipedia should really be informed:

http://en.wikipedia.org/wiki/Recurring_decimal

So should mathforum.org:

http://mathforum.org/library/drmath/view/57041.html

and Wolfram Mathworld:

http://mathworld.wolfram.com/RepeatingDecimal.html

Where did you educate the biology, in toulet?

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#### Nightmare

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##### Re: .99999 does not equal 1
« Reply #42 on: August 10, 2008, 12:13:59 PM »
If a circle exists, then so does .99999=1.
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#### Wendy

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##### Re: .99999 does not equal 1
« Reply #43 on: August 10, 2008, 12:36:51 PM »
Omitting a typing error on behalf of nightmare, he is correct. A circle really only exists in theory, being defined as a polygon with infinite corners. In the same logic, .999... (That is, a decimal with an infinite amount of the number nine behind it, it has to be infinite) only exists in theory, and is theoretically equal to one. There are several explanations to this phenomenon, but I find that the simplest one is that there is no number between .999[repeat] and 1.
Here's an explanation for ya. Lurk moar. Every single point you brought up has been posted, reposted, debated and debunked. There is a search function on this forum, and it is very easy to use.

#### Raist

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##### Re: .99999 does not equal 1
« Reply #44 on: August 10, 2008, 12:41:11 PM »

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#### Nightmare

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##### Re: .99999 does not equal 1
« Reply #45 on: August 10, 2008, 12:41:56 PM »
There was a typo? Meaning the ommision of the "repeat" operator?
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#### Raist

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##### Re: .99999 does not equal 1
« Reply #46 on: August 10, 2008, 12:45:06 PM »
Omitting a typing error on behalf of nightmare, he is correct. A circle really only exists in theory, being defined as a polygon with infinite corners. In the same logic, .999... (That is, a decimal with an infinite amount of the number nine behind it, it has to be infinite) only exists in theory, and is theoretically equal to one. There are several explanations to this phenomenon, but I find that the simplest one is that there is no number between .999[repeat] and 1.
I thought a circle didn't exist because we live in a 3spacial-dimension world. A circle, being a two dimensional figure, has no depth. I've yet to see something without a third dimension.

#### Wendy

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##### Re: .99999 does not equal 1
« Reply #47 on: August 10, 2008, 12:48:33 PM »
Exactly, which means all of this is purely theoretical, but in theory, it is correct. One could actually ask the same question about a sphere, but I don't really know the definition of a perfect sphere.
Here's an explanation for ya. Lurk moar. Every single point you brought up has been posted, reposted, debated and debunked. There is a search function on this forum, and it is very easy to use.

#### lolz at trollz

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##### Re: .99999 does not equal 1
« Reply #48 on: August 10, 2008, 01:15:32 PM »
I don't care how many 9's or how close to 1 it is. Being close, isn't being.
Please write the number you are referring in full, or as a fraction, square root or wrote some other operation (in full) which would result in this number.

Just so we know the exact number you are talking about.

Oh as to a circle existing... well, it doesn't exist as a macroscopic physical object that's for sure.
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#### cmdshft

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##### Re: .99999 does not equal 1
« Reply #49 on: August 10, 2008, 01:46:30 PM »
3/3 = 1

1/3= .33333...

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

.3333 repeating is not a full 1/3.

Yes it is. Do the math on your calculator, and then try to argue the same with it. If you do it again after the argument, tell me if it changed it's answer.

Even my iPod touch 2.0 calculator shows it. If you look, in portrait mode, the calculator is simplistic. It shows the result of the equation 1/3:

In landscape mode, it becomes a scientific calculator, with a more detailed result screen:

There were no alterations done. Simply rotating the device ended up showing more decimal places, revealing that it is actually .33333333...., which is equal to 1/3. So (1/3)+(1/3)+(1/3) = 1. So does (.3333333...) + (.3333333...) + (.3333333...) = (.9999999...) = 1.

Simple.
« Last Edit: August 10, 2008, 01:53:33 PM by Hara Taiki »

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##### Re: .99999 does not equal 1
« Reply #50 on: August 10, 2008, 01:51:58 PM »

#### lolz at trollz

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##### Re: .99999 does not equal 1
« Reply #51 on: August 10, 2008, 02:05:30 PM »
Is this just trolling?
Yes

Lol, why does anyone even need to ask on this forum.  lol
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#### Raist

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##### Re: .99999 does not equal 1
« Reply #52 on: August 10, 2008, 02:18:15 PM »
Exactly, which means all of this is purely theoretical, but in theory, it is correct. One could actually ask the same question about a sphere, but I don't really know the definition of a perfect sphere.
A set of points, whereas all points are equidistant from a point not part of the set.

That is my version of the definition, but i think it is correct.

The definition for a circle isn't an infinite set of vertices, it is the same definition as the spehere but in 2 dimensions.

#### Taters343

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##### Re: .99999 does not equal 1
« Reply #53 on: August 10, 2008, 03:08:46 PM »
In order for two numbers to not be equal, there must be an infinite amount of numbers between them.

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#### rodeoboy

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##### Re: .99999 does not equal 1
« Reply #54 on: August 10, 2008, 03:42:30 PM »
In order for two numbers to not be equal, there must be an infinite amount of numbers between them.

yes, and what is your point...
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#### Roundy the Truthinessist

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##### Re: .99999 does not equal 1
« Reply #55 on: August 10, 2008, 03:49:01 PM »
In order for two numbers to not be equal, there must be an infinite amount of numbers between them.

yes, and what is your point...

If I understand right, he's saying that .999... is equal to 1 because there is not an infinite amount of numbers between them.
Where did you educate the biology, in toulet?

#### Wendy

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##### Re: .99999 does not equal 1
« Reply #56 on: August 10, 2008, 03:57:46 PM »
There isn't even one number between them.
Here's an explanation for ya. Lurk moar. Every single point you brought up has been posted, reposted, debated and debunked. There is a search function on this forum, and it is very easy to use.

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#### cbarnett97

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##### Re: .99999 does not equal 1
« Reply #57 on: August 10, 2008, 04:50:23 PM »
saying .999 repeating = 1 is like saying sqrt(2)=1.4142..... and they are not equal but they are very close and for most calculations it will work but that does not mean that it is correct.
Only 2 things are infinite the universe and human stupidity, but I am not sure about the former.

#### Roundy the Truthinessist

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##### Re: .99999 does not equal 1
« Reply #58 on: August 10, 2008, 05:32:41 PM »
saying .999 repeating = 1 is like saying sqrt(2)=1.4142..... and they are not equal but they are very close and for most calculations it will work but that does not mean that it is correct.

It's not the same at all.  You can't break down sqrt(2) to a definite fraction.  You can however break .333... down to a definite fraction.  Since .333... + .333... +.333... = .999..., it is self-evident (as described before) that .999... = 1.  Some of you "calculus whizzes" could really use a refresher course in basic arithmetic from the looks of things.  Did you look at the sources I provided earlier, cbarnett, that showed that you were wrong about .333... not being equal to 1/3?
Where did you educate the biology, in toulet?

#### Mr. Ireland

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##### Re: .99999 does not equal 1
« Reply #59 on: August 10, 2008, 06:08:57 PM »
Is this just trolling?
Yes

Lol, why does anyone even need to ask on this forum.  lol

I wanted to see narc admit it was and then see if the arguing continued.