Board 8 > .999 = 1. Proof included.

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Xbyte
03/25/12 10:34:00 AM
#1:




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JDTAY
03/25/12 10:36:00 AM
#2:


This better be a rickroll.

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Mik_Pick
03/25/12 10:50:00 AM
#3:


I'm so tired of this debate. :(

And her annoying lisp.

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Westbrick
03/25/12 10:53:00 AM
#4:


"If you don't like it, go to college."

What a snarky, lispy *****.

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Westbrick
03/25/12 10:56:00 AM
#5:


Oh, and here's another gem of a line from this vid:

"The ultimate reason that .999... equals 1 is because it works."

Yes, because truth == practicality. This video is grossly oversimplified, and even if she's right, she's not the best teacher. Also her humor blows.

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tyder21
03/25/12 11:01:00 AM
#6:


From: Westbrick | #006
This video is grossly oversimplified


Not really.

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Metal_DK
03/25/12 11:02:00 AM
#7:


.999~ is = to 1, there is no damn debate about it.

Anyone who says otherwise needs to pay attention to a lecture about infinity and its properties.

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baron von toast
03/25/12 11:04:00 AM
#8:


I got ninety eight point nine repeating problems, but point nine repeating is one.

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Xbyte
03/25/12 11:05:00 AM
#9:


Metal_DK posted...
.999~ is = to 1, there is no damn debate about it.

Anyone who says otherwise needs to pay attention to a lecture about infinity and its properties.


Just deal with it. .999 = 1. Stop arguing.

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OctilIery
03/25/12 11:05:00 AM
#10:


.999 =/= 1.

.999... = 1

And

.999~ = 1

But just .999? No. Learn math before you post this.

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Westbrick
03/25/12 11:06:00 AM
#11:


.999~ is = to 1, there is no damn debate about it.

Anyone who says otherwise needs to pay attention to a lecture about infinity and its properties.


Except that there's plenty of debate about it. When you treat .999 as a normal number susceptible to the rules of basic algebra, then you can perform those proofs we all learned in middle school about how .999 = 1. The real question boils down to whether or not such equations can be performed on an infinite.

This doesn't bother me, though. What does bother me is that they're conceptually incompatible:

.999 -> number infinitely close to 1
1 -> 1

They're not the same, and the saying "save the appearances" applies here.

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XIII_rocks
03/25/12 11:08:00 AM
#12:


I thought it was always accepted that .999 isn't 1, because there's a number between them

but .9999~ is 1 because there isn't. >_>

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OmarsComin
03/25/12 11:09:00 AM
#13:


xbyte = just as awful as strahax

no proof required

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LowCalorieH2O
03/25/12 11:09:00 AM
#14:


if i could only back hand the little hoe that posed this question in the first place

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OctilIery
03/25/12 11:09:00 AM
#15:


.999~ IS NOT 1, but it is EQUAL to 1.

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Westbrick
03/25/12 11:10:00 AM
#16:


I thought it was always accepted that .999 isn't 1, because there's a number between them

but .9999~ is 1 because there isn't. >_>


Yeah, that's one of the proofs used in the video (I believe about halfway through?). Again, it comes into some conceptual difficulty: just because there isn't a number between .999 and 1 doesn't mean they're equal. This belief comes from our inclination to divide things into discrete parts, when- as the video itself emphasizes- this is the wrong way to approach things.

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Ness26
03/25/12 11:11:00 AM
#17:


From: Westbrick | #011
Except that there's plenty of debate about it. When you treat .999 as a normal number susceptible to the rules of basic algebra, then you can perform those proofs we all learned in middle school about how .999 = 1. The real question boils down to whether or not such equations can be performed on an infinite.


Those proofs aren't proofs for the reasons you stated.

One property of real numbers is that for every two real numbers x and y, either x = y or there exists a real number z such that z is between x and y. Using this property you can show that 0.999~ and 1 are equal.

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XIII_rocks
03/25/12 11:12:00 AM
#18:


From: OctilIery | #015
.999~ IS NOT 1, but it is EQUAL to 1.


This is just semantics in any normal conversation

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Westbrick
03/25/12 11:12:00 AM
#19:


.999~ IS NOT 1, but it is EQUAL to 1.

This is just a lexical ambiguity. When people say ".999 is 1," they almost always mean that they're equal. For comparison, your point can be rephrased in different numbers...

1/2 IS NOT .5, but it is EQUAL to .5.

...which isn't what we're talking about.

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VincentLauw
03/25/12 11:13:00 AM
#20:


NO.
NO.
NO.

We are not doing this.

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Westbrick
03/25/12 11:14:00 AM
#21:


Those proofs aren't proofs for the reasons you stated.

One property of real numbers is that for every two real numbers x and y, either x = y or there exists a real number z such that z is between x and y. Using this property you can show that 0.999~ and 1 are equal.


Well-said. So I take if you'd say it follows from this that if the term in question doesn't fall into the realm of real numbers, then this type of proof can't necessarily be applied?

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Ness26
03/25/12 11:14:00 AM
#22:


From: XIII_rocks | #018
This is just semantics in any normal conversation


It's wrong anyway. They are two equivalent ways of expressing the same number.

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LordoftheMorons
03/25/12 11:15:00 AM
#23:


This sure is a topic that needed to exist again

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Westbrick
03/25/12 11:17:00 AM
#24:


...This isn't actually a common B8 topic, is it? Someone fill me in.

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Ness26
03/25/12 11:18:00 AM
#25:


From: Westbrick | #021
Well-said. So I take if you'd say it follows from this that if the term in question doesn't fall into the realm of real numbers, then this type of proof can't necessarily be applied?


0.999~ is real. It has no imaginary component.

If you want something more rigorous (which I've been deliberately trying to avoid), check out things like this:
http://en.wikipedia.org/wiki/Real_number#Completeness

You can apply that directly to show that 0.999~ is real.

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OctilIery
03/25/12 11:18:00 AM
#26:


Ness26 posted...
From: XIII_rocks | #018
This is just semantics in any normal conversation
It's wrong anyway. They are two equivalent ways of expressing the same number.


Not really. They're two different numbers with the same value. They are not the same, but they are equal.

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Tom Bombadil
03/25/12 11:19:00 AM
#27:


From: Westbrick | #024
...This isn't actually a common B8 topic, is it? Someone fill me in.


we have been arguing over this for years

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Ness26
03/25/12 11:19:00 AM
#28:


From: LordoftheMorons | #023
This sure is a topic that needed to exist again


Yeah, considering it's Xbyte and Westbrick I'm aware that there's no hope of actually convincing anyone of anything. I stick with it until their argument breaks down to whining and refusal to accept basic principles.

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Xbyte
03/25/12 11:21:00 AM
#29:


Ness26 posted...
From: LordoftheMorons | #023
This sure is a topic that needed to exist again
Yeah, considering it's Xbyte and Westbrick I'm aware that there's no hope of actually convincing anyone of anything. I stick with it until their argument breaks down to whining and refusal to accept basic principles.


I'm barely posting in this topic, smart guy.

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Ness26
03/25/12 11:22:00 AM
#30:


From: OctilIery | #026
Not really. They're two different numbers with the same value. They are not the same, but they are equal.


I'm pretty sure language like this causes nearly every uniqueness theorem to be broken open.

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OmarsComin
03/25/12 11:23:00 AM
#31:


I'm barely posting in this topic, smart guy.

it's probably for the best

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Xbyte
03/25/12 11:24:00 AM
#32:


OmarsComin posted...
I'm barely posting in this topic, smart guy.

it's probably for the best


Who are you, again?

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Ness26
03/25/12 11:24:00 AM
#33:


From: Xbyte | #029
I'm barely posting in this topic, smart guy.


What can I say, there was so much wrong information in this topic I just assumed you were the one posting it. Sorry.

Your reputation preceded you, I suppose.

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OmarsComin
03/25/12 11:25:00 AM
#34:


it doesn't matter, everyone on this board feels the same way

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Xbyte
03/25/12 11:25:00 AM
#35:


Ness26 posted...
From: Xbyte | #029
I'm barely posting in this topic, smart guy.
What can I say, there was so much wrong information in this topic I just assumed you were the one posting it. Sorry.

Your reputation preceded you, I suppose.


hurrrr hurrrrr hurrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr

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SpeedYoshi
03/25/12 11:31:00 AM
#36:


thank god there's a troll on this board for this argument

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Takfloyd_mkII__
03/25/12 11:39:00 AM
#37:


0.999~ isn't = 1 until someone counts all the 9s to see if there's room for another number between them.

Any volunteers?
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special_sauce
03/25/12 12:13:00 PM
#38:


In other news, I just fell in love with this chick in this video.



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tereziWright
03/25/12 12:17:00 PM
#39:


wait

Xbyte ISN'T Strahax?

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JDTAY
03/25/12 12:20:00 PM
#40:


Still disappointed that this wasn't a rickroll.

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Westbrick
03/25/12 12:34:00 PM
#41:


Yeah, considering it's Xbyte and Westbrick I'm aware that there's no hope of actually convincing anyone of anything. I stick with it until their argument breaks down to whining and refusal to accept basic principles.

Whoa now, do I have a reputation here already? Sweet.

Clearly this is something that's going nowhere fast, and there are people better at and more studied in mathematics than I here, so I'll defer. The conceptual friction is troubling, but it's not worth getting riled up about.

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mnkboy907
03/25/12 12:38:00 PM
#42:


And here I thought B8 was above CE. Oh well.

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ViviffTheMobile
03/25/12 12:42:00 PM
#43:


I've always wondered then why .99~8 (9s repeating with an 8 on the end) isn't then equal to .999~ which is equal to 1, and then you work forward backward through all the numbers infinitely like that and then all numbers equal all other numbers.

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SpeedYoshi
03/25/12 12:44:00 PM
#44:


because .999~8 isn't a real number

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Ness26
03/25/12 12:45:00 PM
#45:


From: ViviffTheMobile | #043
I've always wondered then why .99~8 (9s repeating with an 8 on the end)


Your number is ill-defined. You say you're putting an 8 on the end... but there is no end.

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SovietOmega
03/25/12 12:47:00 PM
#46:


XD watching her fibonacci stuff. slug cats <3<3<3

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ViviffTheMobile
03/25/12 12:52:00 PM
#47:


Ah, very good. I see my liberal arts degree is showing, so I'll just show myself out.

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Forceful_Dragon
03/25/12 12:54:00 PM
#48:


I love Vihart videos. FD approves of this topic.

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Red Shifter
03/25/12 12:57:00 PM
#49:


999/1000 is not 1

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Forceful_Dragon
03/25/12 1:00:00 PM
#50:


From: Red Shifter | #049
999/1000 is not 1




but 999.999999999999999999~ / 1000 is 1.

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