.99999 does not equal 1

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Re: .99999 does not equal 1
« Reply #420 on: August 20, 2008, 08:27:16 AM »
Occam's Razor has nothing to with Mathematics!

Which is exactly why he'd use it in mathematics.

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Sean O'Grady

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Re: .99999 does not equal 1
« Reply #421 on: August 20, 2008, 08:31:06 AM »
18 pages...

0.99999 != 1
0.999...  = 1

[NOTE: THIS POST WILL BE SPAMMABLE SHOULD STUPIDITY CONTINUES BEYOND PAGE 18]

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zeroply

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Re: .99999 does not equal 1
« Reply #422 on: August 20, 2008, 12:48:06 PM »
I thought about it and my first answer was incomplete and based on an assumption.

There is not enough information present in the statement to say clearly that 0.9999... <> 1

We are all assuming that both numbers are real. But if they are in *R (hyperreals), then 1.000... - 0.999... would be an infinitesimal but not equal to zero. I'm going to abuse notation here to avoid Dedekind cut type construction, but 1.000...1 and 1.0000...2 would be perfectly good hyperreals which are distinct in *R but which would not be differentiated in R since they lie in the hyperreal "cloud" around 1.

I'm not an expert in nonstandard analysis, any math geeks here please feel free to chime in or shoot me down.

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narcberry

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Re: .99999 does not equal 1
« Reply #423 on: August 20, 2008, 03:42:43 PM »
It's true, there is an infinitesimally small number between 0.999... and 1.
If you take the position that infinities cannot exist (this includes the infinitesimals), then you are simply mistaken.


Put another way:
Given a line of finite size, how many times can it be divided? If you say an infinite amount of times, then you are assuming infinitesimally small line segments are possible. You cannot divide the line an infinite amount of times without creating at least one segment with a size of (1 - 0.999...).

Furthermore an infinite amount of line segments of length (1 - 0.999...), assuming 0.999... = 1, would be of 0 length. This means if 0.999... = 1 then dividing a line into an infinite amount of equal segments would yield an infinite amount of segments of length 0. Since the total line length is the sum of its parts, you would have infinity * 0 = a finite number.

In other words
0.999... = 1   -> infinity * 0 = x | x is some finite number.
« Last Edit: August 20, 2008, 03:47:42 PM by narcberry »

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Wendy

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Re: .99999 does not equal 1
« Reply #424 on: August 20, 2008, 03:55:45 PM »
It's true, there is an infinitesimally small number between 0.999... and 1.

No it's not.
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.

Re: .99999 does not equal 1
« Reply #425 on: August 20, 2008, 08:50:54 PM »
0.111... = 1/9
0.222... = 2/9
0.333... = 3/9
0.444... = 4/9
0.555... = 5/9
0.666... = 6/9
0.777... = 7/9
0.888... = 8/9
0.999... = 9/9 = 1
1.111... = 1 1/9

etc...

Except you skip 1.0000...  ::)
And thus you descend into the realm of stupidity.

You clearly don't accept that 0.111...=1/9

so, our pattern
0.111...
0.222...
0.333...
0.444...
0.555...
0.666...
0.777...
0.888...
0.999...

shows an increase of 0.111... between each step. Which value should come next? Since you don't accept that 0.111...=1/9, let's try it with definite numbers:

0.111111111
0.222222222
0.333333333
0.444444444
0.555555555
0.666666666
0.777777777
0.888888888
0.999999999

Between each step, we have an increase of 0.111111111

Therefore, 0.999999999 + 0.111111111 = 1.11111111 and this number is the next one in the sequence.

Since you (obviously) don't know anything about mathematics, you thought instinctively that the next number in the sequence was 1.00000000. Naturally you were wrong. Like you have been wrong in this thread. Over and over.

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Parsifal

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Re: .99999 does not equal 1
« Reply #426 on: August 20, 2008, 08:53:01 PM »
This thread is full of troll food.
I'm going to side with the white supremacists.

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mwahaha

Re: .99999 does not equal 1
« Reply #427 on: August 20, 2008, 09:05:09 PM »

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Parsifal

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Re: .99999 does not equal 1
« Reply #428 on: August 20, 2008, 09:06:52 PM »
Why isn't that hand connected to a wrist?
I'm going to side with the white supremacists.

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mwahaha

Re: .99999 does not equal 1
« Reply #429 on: August 20, 2008, 09:08:09 PM »
Just noticed that...idk.

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zeroply

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Re: .99999 does not equal 1
« Reply #430 on: August 20, 2008, 09:15:32 PM »
It's true, there is an infinitesimally small number between 0.999... and 1.
If you take the position that infinities cannot exist (this includes the infinitesimals), then you are simply mistaken.

Again, ONLY if you are talking about hyperreal numbers here. If 0.999... and 1 are reals then they are exactly the same. If 0.999... is a hyperreal (and obviously a member of R - *R ) then we're cool. We've basically picked a point in the hyperreal cloud around 1.

Put another way:
Given a line of finite size, how many times can it be divided? If you say an infinite amount of times, then you are assuming infinitesimally small line segments are possible. You cannot divide the line an infinite amount of times without creating at least one segment with a size of (1 - 0.999...).

Nope - this doesn't work. There will be a bijective correspondence between R and the length of any finite line segment. Consider the division of the line by first breaking it at 1/2, then 1/4, then 1/8 and so on. Our resulting line segments will be [1,1/2], [1/2, 1/4], [1/4,1/8], and so on. For EVERY line segment [1/2^n, 1/2^(n+1)] we have some real distance. No way to bring an infinitesimal into the mix.

Furthermore an infinite amount of line segments of length (1 - 0.999...), assuming 0.999... = 1, would be of 0 length. This means if 0.999... = 1 then dividing a line into an infinite amount of equal segments would yield an infinite amount of segments of length 0. Since the total line length is the sum of its parts, you would have infinity * 0 = a finite number.

This doesn't prove anything at all. Assume that 1=0.999... and therefore 1-0.999...=0

Consider the infinite set of line segments [x,x] where 0 < x < 1, then each segment has length 0.

Then their union is (0,1) and has length 1. So this holds anyway and is irrelevant to the discussion.

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zeroply

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Re: .99999 does not equal 1
« Reply #431 on: August 20, 2008, 09:19:07 PM »
This thread is full of troll food.

Well, maybe you're not getting anything out of it, but it's given me an excuse to review my books on analysis so I'm happy as a clam.

Re: .99999 does not equal 1
« Reply #432 on: August 20, 2008, 09:20:03 PM »
(snip)

Put another way:
Given a line of finite size, how many times can it be divided? If you say an infinite amount of times, then you are assuming infinitesimally small line segments are possible. You cannot divide the line an infinite amount of times without creating at least one segment with a size of (1 - 0.999...).

Furthermore an infinite amount of line segments of length (1 - 0.999...), assuming 0.999... = 1, would be of 0 length. This means if 0.999... = 1 then dividing a line into an infinite amount of equal segments would yield an infinite amount of segments of length 0. Since the total line length is the sum of its parts, you would have infinity * 0 = a finite number.

In other words
0.999... = 1   -> infinity * 0 = x | x is some finite number.
You don't understand infinity at all, do you? Hint: there are all kinds of infinities. None of them prove what you want them to prove.

Between the numbers 0 and 0.1 there's an infinite amount of real numbers (not even using repeating decimals, or hyperreality or anything else). And none of them equal the supposed difference between 0.999... and 1.

And your supposed "proof"? Is as contradictory as hell. In one sentence you say, by creating an infinite number of segments from your line you'd create at "least one segment with a size of (1 - 0.999...).". That sentence means that you are assuming that 1<>0.999... Two sentence later you contradict your own assumption by saying "(...) this means if 0.999... = 1 (...)".

You can't have your cake and eat it too.


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zeroply

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Re: .99999 does not equal 1
« Reply #433 on: August 20, 2008, 09:21:38 PM »
If 0.999... is a hyperreal (and obviously a member of R - *R ) then we're cool.

Sorry, this should be *R - R

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Parsifal

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Re: .99999 does not equal 1
« Reply #434 on: August 20, 2008, 09:24:33 PM »
Well, maybe you're not getting anything out of it, but it's given me an excuse to review my books on analysis so I'm happy as a clam.

Me too. It's just that DigCamara doesn't seem to realise that Narcberry is a troll.
I'm going to side with the white supremacists.

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WardoggKC130FE

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Re: .99999 does not equal 1
« Reply #435 on: August 21, 2008, 12:19:53 AM »
You can't have your cake and eat it too.

Why?  That's the only way I like to have my cake.  Doesn't do me a damn bit of good just sitting there in front of me.

Re: .99999 does not equal 1
« Reply #436 on: August 21, 2008, 01:00:52 AM »
of course it doesn't equal one.
but why does it matter?
you'll never have .99999 of anything.
the world, flat and round, works in whole numbers.


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crazybmanp

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Re: .99999 does not equal 1
« Reply #437 on: August 21, 2008, 01:03:57 AM »
let me break this down
1/3=~.33333333
3/3=~.99999999
1=~.999999999

that is the correct answer, not 1=.9999999, that is impossible
1=~.9999999999 (one equals approximately point nine repeating)

in wich case 1 does not equil .9999999

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Parsifal

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Re: .99999 does not equal 1
« Reply #438 on: August 21, 2008, 01:04:36 AM »
of course it doesn't equal one.
but why does it matter?
you'll never have .99999 of anything.
the world, flat and round, works in whole numbers.

So pi is equal to 3, is it? And I take it that we feel g as exactly 10 m s-2?
I'm going to side with the white supremacists.

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Parsifal

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Re: .99999 does not equal 1
« Reply #439 on: August 21, 2008, 01:05:40 AM »
let me break this down
1/3=~.33333333
3/3=~.99999999
1=~.999999999

that is the correct answer, not 1=.9999999, that is impossible
1=~.9999999999 (one equals approximately point nine repeating)

in wich case 1 does not equil .9999999

1 does not equal 0.9999999, you are correct. However, it does equal 0.999..., where the ellipsis indicates an infinite sequence of 9s.
I'm going to side with the white supremacists.

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crazybmanp

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Re: .99999 does not equal 1
« Reply #440 on: August 21, 2008, 01:07:27 AM »
let me break this down
1/3=~.33333333
3/3=~.99999999
1=~.999999999

that is the correct answer, not 1=.9999999, that is impossible
1=~.9999999999 (one equals approximately point nine repeating)

in which case 1 does not equal .9999999

1 does not equal 0.9999999, you are correct. However, it does equal 0.999..., where the ellipsis indicates an infinite sequence of 9s.

i never said  1=.9999999 i said 1=~.999999999 please note the approximately sign

Re: .99999 does not equal 1
« Reply #441 on: August 21, 2008, 01:08:03 AM »
when do you use pi outside of mathematics and theory?

gravity is relative.

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WardoggKC130FE

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Re: .99999 does not equal 1
« Reply #442 on: August 21, 2008, 01:10:21 AM »

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Jack

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Re: .99999 does not equal 1
« Reply #443 on: August 21, 2008, 01:11:01 AM »
18 pages...

0.99999 != 1
0.999...  = 1

[NOTE: THIS POST WILL BE SPAMMABLE SHOULD STUPIDITY CONTINUES BEYOND PAGE 18]

Re: .99999 does not equal 1
« Reply #444 on: August 21, 2008, 01:15:32 AM »
nice whut picture!

but to explain

gravity is relative to where you are.
it changes if i'm here, in space, on mars, on the other side of this flat earth  ::), or anywhere else in the universe.
so you can't use that as a constant.

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Parsifal

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Re: .99999 does not equal 1
« Reply #445 on: August 21, 2008, 01:17:10 AM »
1 does not equal 0.9999999, you are correct. However, it does equal 0.999..., where the ellipsis indicates an infinite sequence of 9s.

i never said  1=.9999999 i said 1=~.999999999 please note the approximately sign

I am well aware of what you said, please note the bolded and enlarged text.

when do you use pi outside of mathematics and theory?

gravity is relative.

You are stupid, please leave and never come back. Thank you.
I'm going to side with the white supremacists.

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Parsifal

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Re: .99999 does not equal 1
« Reply #446 on: August 21, 2008, 01:22:22 AM »
gravity is relative to where you are.
Sadly, gravity doesn't exist. GTFO and debate in the sticky "gravity".

He's right, you know. The force of gravity you feel is a linear function of your position in the Universe, since there are real numbers a, b, c and d such that:

Fg = ax + by + cz + dt
I'm going to side with the white supremacists.

Re: .99999 does not equal 1
« Reply #447 on: August 21, 2008, 01:24:40 AM »
Robosteve is the one who brought up the idea of gravity in this debate, not me.

and Robosteve also dodged the question.


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Jack

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Re: .99999 does not equal 1
« Reply #448 on: August 21, 2008, 01:25:25 AM »
He's right, you know. The force of gravity you feel is a linear function of your position in the Universe, since there are real numbers a, b, c and d such that:

Fg = ax + by + cz + dt
I never said he was wrong.

Re: .99999 does not equal 1
« Reply #449 on: August 21, 2008, 01:27:54 AM »
Think of it this way:

the difference between 0.99 and 1 is 0.01
the difference between 0.9999999999 is 0.0000000001
the more 9's there are, the closer to zero the difference becomes

if there are an infinite number of 9's, the difference is infinitely close to zero.

now, ladies and gentlemen, how big is a number infinitely close to zero?
hint: it's fucking zero!

In other words, there is zero difference between 1, and 0.9999999999..........