Board 8 > .999 = 1. Proof included.

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ToukaOone
03/25/12 1:06:00 PM
#51:


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

The snow is white if and only if the snow is white.
The snow is not not white if and only if the snow is white.

Is the first sentence always true so long as you keep using the form X IFF X?

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foolm0ron
03/25/12 1:15:00 PM
#52:


From: Westbrick | #011
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.


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

There, does that make you happy? Saying a real number is infinitely close to another number is the equivalent of saying they are equal.

Anyways, I love these topics because of the ridiculous logic that gets posted to troll all the super serious people who think there still exists people who don't believe this. Viviff's post is my fav so far./

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azuarc
03/25/12 2:25:00 PM
#53:


foolm0ron posted...
Anyways, I love these topics because of the ridiculous logic that gets posted to troll all the super serious people who think there still exists people who don't believe this. Viviff's post is my fav so far./


Except for one thing...

I'm a math teacher. There ARE people who don't believe this. I meet them routinely in the real world. Because I meet enough real people who are stupid, I'm not convinced that the imaginary people on the internet aren't. (People I know both on the internet and IRL are complex.)
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ViviffTheMobile
03/25/12 2:34:00 PM
#54:


Hey mathematical theory isn't my strong point! I approached it philosophically! Plus I wasn't offering a proof/argument of why it was wrong; at this point to deny its truth would be asinine and stubborn. I was just wondering why that situation doesn't occur.

So many people hit the brick wall because their brains are hardwired at this point to understand that 2 decimal numbers cannot represent the same value. Much like most people assume all metal is ferromagnetic. Once you look into it and remove yourself from your belief (AKA critical thinking), yes it becomes a truth to embrace.

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MrGreenonion
03/25/12 2:51:00 PM
#55:


From: Westbrick | #011
Except that there's plenty of debate about it.


No there isn't. There's just angry people who don't know things.

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Westbrick
03/25/12 2:54:00 PM
#56:


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

There, does that make you happy?


Obviously not! 1 is not "infinitely close" to 1; it is 1. And the idea that people who question the conceptual incongruity between the terms are "stupid" is just silly.

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LordoftheMorons
03/25/12 2:59:00 PM
#57:


Sure it is, I have a sequence (a_n) with a_n=1 for all n, and for any epsilon>0, I can find N such that |a_n-1|<epsilon for n>N. That's what it means for two things to be infinity close. The exact same would apply if I took a_n to be .99999...9 (n 9's).

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Westbrick
03/25/12 3:01:00 PM
#58:


I get that. There's no doubt that the proof checks out (and I'd certainly hope no one would question this), but it's the conceptual aspect that's troubling.

For those who believe that .999 = 1 is trivially obvious or whatever, here's a question: how, if at all, does this impact the resolution of Zeno's "Achilles and the Tortoise" paradox?

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ToukaOone
03/25/12 3:07:00 PM
#59:


What do you mean by conceptual aspect?

Seriously, why do you think that they wouldn't be the same, despite all these 'mathy' proofs? I'm not fishing for a 'oh... I don't know', but rather 'I believe this for reasons X Y and Z'

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firefdr
03/25/12 3:08:00 PM
#60:


damn stupid people

this is worse than religious debates
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Ness26
03/25/12 3:11:00 PM
#61:


Infinity is not something that easily makes sense conceptually. Consider the Hilbert Hotel.

http://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel

Basically you consider a Hotel with an infinite but countable number of rooms. That is, it has a Room #1, Room #2, Room #3, and so on, such that there is a room corresponding to every positive integer. Every room of the hotel is occupied.

The paradox is that even though every room in the hotel is occupied, you can still accommodate a new guest. If a new guest comes, simply tell everyone to move one room down. The new guest can then take Room #1.

The hotel can also hold 2 new guests -- tell everyone to move down 2 rooms. You can extend this to say that the hotel can hold any finite number of guests by having the current guests move down a certain number of rooms.

The hotel can also hold INFINITE additional guests. If we have an infinite (but countable) number of guests arrive, have the current guests occupy only the even numbered rooms. There are infinitely many even numbered rooms, so all can be accounted for. And now we have all of the odd numbered rooms free, and there are infinitely many of those so we can assign our new guests to those rooms.

So yes, it is normal for it to be confusing to get your head around the idea.

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X_Dante_X
03/25/12 3:18:00 PM
#62:


what an annoying hotel to stay out, they constantly make you switch rooms

I'm imagining getting a call at like 3 in the morning, and them being all YOU GOTTA MOVE DOWN THE HALL

and then the process happens again ten minutes later

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Westbrick
03/25/12 3:26:00 PM
#63:


So yes, it is normal for it to be confusing to get your head around the idea.

This is literally all I'm saying. Christ.

As someone who's perfectly familiar with all the proofs of .999 = 1 and has been for years, the one thing I have learned from this topic is that people take their trivial math proofs very, very seriously.

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foolm0ron
03/25/12 3:34:00 PM
#64:


From: Westbrick | #056
Obviously not! 1 is not "infinitely close" to 1; it is 1. And the idea that people who question the conceptual incongruity between the terms are "stupid" is just silly.


Yes, you are stupid if you are presented with step-by-step explanations for why "infinitely close to" is the same as "equals", and you STILL somehow don't understand it.

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tyder21
03/25/12 3:39:00 PM
#65:


From: X_Dante_X | #062
what an annoying hotel to stay out, they constantly make you switch rooms

I'm imagining getting a call at like 3 in the morning, and them being all YOU GOTTA MOVE DOWN THE HALL

and then the process happens again ten minutes later


It would be even more annoying if 2 to the power of the number of people in the hotel showed up. The managers would be confused because no matter where they moved you, they would never be able to fit all the people inside of the hotel.

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

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X_Dante_X
03/25/12 3:42:00 PM
#66:


I'd be chill with that - they'd be so concerned trying to figure it out, they wouldn't kick me out of my room and I could get some rest

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Westbrick
03/25/12 3:50:00 PM
#67:


Yes, you are stupid if you are presented with step-by-step explanations for why "infinitely close to" is the same as "equals", and you STILL somehow don't understand it.

Please explain to me, in words, why "infinitely close to" means "is the same as." We all understand that the proofs work out this way, but, as has been shown time and time again in this topic, anything involving infinity is going to be incredibly hard to wrap one's head around.

And do try and keep the language toned down. We're just talking about math, no need to call people stupid.

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rocket157
03/25/12 3:53:00 PM
#68:


This is still a debate? Also, I actually did enjoy the video.


*blastin' off, yo*

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foolm0ron
03/25/12 3:54:00 PM
#69:


From: Westbrick | #067
Please explain to me, in words, why "infinitely close to" means "is the same as." We all understand that the proofs work out this way, but, as has been shown time and time again in this topic, anything involving infinity is going to be incredibly hard to wrap one's head around.


Sure, so you just want more detail in the proof to be convinced. That is fine, and isn't an indication of stupidity.

Well here's the best way to explain it. Think of any 2 different real numbers (decimal numbers). Now think of a number in between those 2 numbers. It's ALWAYS possible, right?
Now think of 2 equal real numbers, 2.5 and 2.5 or something. Try to think of a number between those 2 numbers. Impossible, right?

Now try to think of a number between .999 repeating and 1. Impossible, right? That's because .999 repeating is infinitely close to 1, so there does not exist a number between it and 1. Therefore they are equal, and that's why infinitely close is equivalent to equality.

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Westbrick
03/25/12 3:55:00 PM
#70:


Another thing worth pointing out for all the smart people in this topic: .999 = 1 ultimately means that they're both notations for the same thing, much like 1/2 and .5. It does not mean that a series which gradually approaches some number at an infinite rate necessarily reaches that number. Many people wrongly infer that .999 = 1 serves as a solution to Zeno's paradoxes (which is equally untrue of calculus, for other reasons).

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PurpleMonkDish
03/25/12 4:01:00 PM
#71:


From: Westbrick | #070
Another thing worth pointing out for all the smart people in this topic: .999 = 1 ultimately means that they're both notations for the same thing, much like 1/2 and .5. It does not mean that a series which gradually approaches some number at an infinite rate necessarily reaches that number. Many people wrongly infer that .999 = 1 serves as a solution to Zeno's paradoxes (which is equally untrue of calculus, for other reasons).


You have this inane belief that numbers "approach" or "reach" other numbers. They don't. Numbers don't move. They just are.

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Westbrick
03/25/12 4:10:00 PM
#72:


You have this inane belief that numbers "approach" or "reach" other numbers. They don't. Numbers don't move. They just are.

Um? This is what series do. When you have a series of numbers, say 1/2 + 1/4 + 1/8 + ... that's outlined roughly in Zeno's paradoxes, then the result does indeed "approach" others.

Just to clarify, people in my own personal experiences have used .999 = 1, a concept which is already a little confusing thanks to its involvement of the infinite, to make claims far beyond what they're entitled to. But apparently this makes me both "stupid" and "inane." You people take math more seriously than politics!

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tyder21
03/25/12 4:18:00 PM
#73:


From: Westbrick | #072
You people take math more seriously than politics!


It's certainly more interesting.

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Westbrick
03/25/12 4:29:00 PM
#74:


.999 = 1 is interesting? If you say so. I'm not even sure what the truth value of this assertion is, despite a notational clarification. Does it actually find practical application, or is it more an idle thought experiment?

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agesboy
03/25/12 4:35:00 PM
#75:


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



oh my god möbiaboros

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SovietOmega
03/25/12 5:10:00 PM
#76:




i can't get enough of these...

e to the i to the e i o equals e to the wau to the tau wau wau~

she is so cute when she trolls us XD <3

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Forceful_Dragon
03/25/12 5:12:00 PM
#77:


did you just discover Vihart ITT Omega?

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SovietOmega
03/25/12 5:14:00 PM
#78:


because of this topic, yes.

i have no regrets.

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ZX_Lucian
03/25/12 5:20:00 PM
#79:


Debates are garbage! CRUNCH!

I'll add it...to...never mind.

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The Real Truth
03/25/12 5:21:00 PM
#80:


I love these topics because it's a bunch of people arguing about nothing, and other trying to purposely annoy those people.

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rychu_supadude
03/25/12 6:03:00 PM
#81:


The main thing this topic proves is that math is more awesome than science.
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dinobot19
03/25/12 6:17:00 PM
#82:


.999 doesn't equal 1, topic title is a lie



(I'm sure people pointed out the lack of dots way earlier but I don't feel like reading)

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