/sci/ - Science & Math

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Anonymous Thu Aug 22 14:29:40 2013 No.5984756 [DELETED]

Hey /sci/, why do mathematicians believe that 0.999... = 1 ?

Even a 6th grader could disprove it.
Allow me to demonstrate.
1 - 0.000...1 = 0.999... = 1
However, 0.999... - 0.000...1 = 0.999...8, which decisively != 1. How do mathematicians make this mistake all the time, and then claim that they're great at math?!

>pic related, it's mathematicians' response when anyone dares challenge their narrow-minded (AND WRONG) views of math

>>	Anonymous Thu Aug 22 14:31:10 2013 No.5984761 Also, not trolling, genuinely curious as to how people who are self-proclaimed masters in their field can ignore such an obvious logical conclusion

>>	Anonymous Thu Aug 22 14:34:40 2013 No.5984768 You can't have a number after an infinite string of numbers, if it never ends where would you find the 8

>>	Anonymous Thu Aug 22 14:35:10 2013 No.5984769 >>5984756 .000....1? As in, an infinite number of zeros,and then AFTER that INFINITE number of zeros, a 1? Do you see how that number could not exist?

>>	Anonymous Thu Aug 22 14:44:39 2013 No.5984785 >>5984769 It's just a notation. Like 0.999... Or do you think a number with infinite 9s can LITERALLY exist?

Anonymous Thu Aug 22 14:47:10 2013 No.5984788

>>5984785

See, but .999.... doesn't defy definitions. It's expressible mathematically, and is consistent with mathematical definitions.

.000.....1 is not. There is a class of numbers where in they can be invoked (Read: Hyperreal numbers), but it's not the standard real numbers.

>>	Anonymous Thu Aug 22 14:48:09 2013 No.5984792 >>5984788 0.000...01 can be rigorously defined as the limit of (1/10)^n as n goes to infinity. Consistent and logical.

>>	Anonymous Thu Aug 22 14:49:10 2013 No.5984793 >>5984792 That limit is 0.

>>	Anonymous Thu Aug 22 14:51:07 2013 No.5984797 >>5984793 If 0.999.. is a notation for 1, then 0.00...01 is a notation for 0.

>>	Anonymous Thu Aug 22 14:51:07 2013 No.5984798 Here ya go dum dum http://www.youtube.com/watch?v=TINfzxSnnIE

>>	Anonymous Thu Aug 22 14:51:37 2013 No.5984799 >>5984756 doesn't even know whats happening in the pic just ignore the troll

>>	Anonymous Thu Aug 22 14:53:36 2013 No.5984805 >>5984797 Well, .000...1 being 0 is a non-sensical representation for that number, but if that's the case, then 1-.000...1=.999.... Is equivalent to 1=.999.... So you agree that they are the same number.

>>	Anonymous Thu Aug 22 14:55:05 2013 No.5984808 >>5984798 http://www.youtube.com/watch?v=wsOXvQn3JuE

>>	Anonymous Thu Aug 22 15:03:06 2013 No.5984820 >>5984756 >0.000...1 At best you're defining a finite number of digits, which isn't he same thing as 0.999...

>>	Anonymous Thu Aug 22 15:06:36 2013 No.5984824 >>5984805 #rekt

>>	Anonymous Thu Aug 22 15:07:05 2013 No.5984825 >1 - 0.000...1 = 0.999... = 1 First step is wrong. Any conclusions therefore are not correct If you do 1-0.999999, what is the last digit? You assume it is 1, but the last digit is 0 (ie. there is no last digit).

>>	Anonymous Thu Aug 22 15:13:36 2013 No.5984834 >>5984768 at the end

>>	Anonymous Thu Aug 22 16:04:05 2013 No.5984917 File: 34 KB, 413x395, draper.jpg [View same] [iqdb] [saucenao] [google] >>5984792 <span class="math">0.999...=\lim_{n\to\infty}1-\frac{1}{10^n}=1[/spoiler]

>>	Anonymous Thu Aug 22 16:05:05 2013 No.5984923 >>5984792 >>5984917 By the way, the scoffing Draper was meant for everybody else

>>	Anonymous Thu Aug 22 23:13:26 2013 No.5985700 >>5984917 Neat.

>>	Anonymous Thu Aug 22 23:16:26 2013 No.5985708 .000...1 is not a number. You can't have something following an infinite amount of something else otherwise you wouldn't have an infinite amount of zeros anymore, get it?

>>	Anonymous Thu Aug 22 23:37:26 2013 No.5985749 >1/3 = 0.333333333......... >1/3 + 1/3 = 0.33333.... + 0.333333..... = 0.66666..... = 2/3 >2/3 + 1/3 = 0.666666.... + 0.3333333..... = 0.9999999..... = 3/3 = 1 Therefore, 0.9999999999........ = 1

Anonymous Fri Aug 23 00:02:28 2013 No.5985778

>>5985749

Let me just save us all a head ache that we all know is coming.

What this person has done does not constitute a rigorous proof. It is a great way to show that there's some logical reasons to believe that the seemingly impossible statement 1=.999.... statement is true.

Rigorous proofs do exist (Of particular note, the formula for evaluating an infinite geometric series).

>>	Anonymous Fri Aug 23 00:07:55 2013 No.5985788 >>5984768 There could be an infinite amount of numbers between the end number and the start one dingus.

Anonymous Fri Aug 23 00:13:56 2013 No.5985795

>>5985788

No, there can't be, because then your "end number" would be AFTER an infinite number of digits.

Infinite means without termination, after means once termination has happened, they literally contradict each other if you use them simultaneously.

>>	Anonymous Fri Aug 23 00:20:57 2013 No.5985804 >>5984785 Dude, you are a moron. ... implies infinity. You can't have infinity and then something after that.

>>	Anonymous Fri Aug 23 00:21:26 2013 No.5985805 >>5985788 This is where you are wrong.

Anonymous Fri Aug 23 00:26:26 2013 No.5985812

>>5985788
The property of having an "end" is intrinsic of termination, which is intrinsic to finite numbers. For any infinite number, there is no termination, thus no end can be found.

1/3 = 0.333...
0.333...*3 = 0.999...
1/3*3 = 1
Thus 0.999... = 1
QED.

Anonymous Fri Aug 23 00:27:56 2013 No.5985813

>>5984756
Yes, it seems illogical for 0.999... to equal one, but first we have to look at how we define are number system. One of the ways we define two different numbers is if there is a number between them. Now here's the kicker, there is nothing between 0.999... and 1. So, logically, yes, 1 does not equal 0.999.... However, with the way that set of numbers is defined, they are the same thing.

>>	Anonymous Fri Aug 23 00:29:26 2013 No.5985815 >>5985813 Mathematics is the very foundation of logic. When you say "logic", you really mean your own troglodyte senses.

>>	Anonymous Fri Aug 23 00:29:26 2013 No.5985816 >>5985795 Not the person you're responding to. You clearly do not understand what math is, and what math is not.

Anonymous Fri Aug 23 00:30:55 2013 No.5985818
File: 26 KB, 300x369, Omega-exp-omega-labeled.svg.png [View same] [iqdb] [saucenao] [google]

>>5985708
>You can't have something following an infinite amount of something else
Sure you can — this is true of every infinite ordinal number except ω, which is the order type of the natural numbers. But by definition, a sequence has order type ω, so that's the reason why there can't be any digits occurring at infinite index.

Pic related: the ordinal <span class="math">\omega^\omega[/spoiler].

>>	Anonymous Fri Aug 23 00:31:26 2013 No.5985820 >>5985816 Care to enlighten me then?

Anonymous Fri Aug 23 00:32:26 2013 No.5985822

>>5985812

You're making assumptions about reality and thus math. Math is conceptual and plays by man-invented rules that mimic reality. But when you can only make assumptions about reality (Especially with Occam's razor of all things, lol), math becomes metaphorical again. Which is what it should be.

Anonymous Fri Aug 23 00:32:55 2013 No.5985821

>>5985815
No, I mean that by calling an orange an apple, you are wrong. To someone that knew what the world "equals" means, but didn't know our number system, if you were to ask them DOES 0.999... EQUAL 1. If they had any intelligence whatsoever, they would say no. However, although I agree with you that math is the very foundation of logic, the way that that particular set is defined, doesn't really fit. It's an inconsistency. Not an illogical one, but an inconsistency nonetheless.

Anonymous Fri Aug 23 00:36:56 2013 No.5985824

>>5985821
Now you're confusing different symbols representing the same values with different values. This is a common error among the low IQ.

No one in this thread, or anywhere in the mathematical community, have ever claimed that the symbols of 0.999... and 1 lack differentiation. For one, they have a tremendous difference in number of strokes. But this is not the issue, the issue is value, which is the only thing the equals sign deals with.

What you're saying is as moronic as if someone would exclaim that 2/2 does not equal 1 simply because the symbols are different, when they are as mathematically identical as 0.999... and 1.

>>	Anonymous Fri Aug 23 00:43:26 2013 No.5985830 File: 46 KB, 304x304, billy-joel.jpg [View same] [iqdb] [saucenao] [google] >>5985820 >0 replies just responding to let you know that you won the argument congrats

Anonymous Fri Aug 23 00:45:26 2013 No.5985834

>>5985824
Except 2/2, using defined processes, can be turned into 1. .999... can not turn into 1 through an equation or process. It is simply that since there is no other number between them, they are the same number, because that is how the set is defined. Why are you attacking me personally with quotes such as "This is a common error among the low IQ.", using a strawman arguement, and even then not fully understanding what I was saying.

Why don't you read the 'proofs from the construction of the real numbers' paragraph in http://en.wikipedia.org/wiki/0.999......

>>	Anonymous Fri Aug 23 01:12:26 2013 No.5985862 >>5984756 >0.00...1 >logic

>>	Anonymous Fri Aug 23 05:28:04 2013 No.5986073 >>5984798 So at the very end we still can't have a nice set, but only an ugly proper class. Bagh

>>	Anonymous Fri Aug 23 05:36:34 2013 No.5986078 >>5985834 But actually it can 1/3 = 0.333... 1/33 = 0.333...3 = 3/3 = 0.999... = 3/3 = 1

>>	Anonymous Fri Aug 23 06:29:04 2013 No.5986116 Is 0.9 equal to 1? No. Is 0.99 equal to 1? No. Is 0.999999 equal to 1? No. Is 0.999... equal to 1? No.

>>	Anonymous Fri Aug 23 07:05:34 2013 No.5986163 If we assume that 0.999... = x 0.999... = x We times by 10 9.999 = 10x We subtract 1x 9 = 9x Divide by 9 9 / 9 = 9x / 9 1 = x

>>	Anonymous Fri Aug 23 08:00:04 2013 No.5986215 >>5985812 but 1/3 =/= 0.333... because 0.333...*3 = 0.999... =/= 1

>>	Anonymous Fri Aug 23 08:09:04 2013 No.5986217 >>5986215 And that's, kids, how you properly use circular logic.

>>	Anonymous Fri Aug 23 08:13:34 2013 No.5986220 >>5986215 Looks at >>5986163

>>	Anonymous Fri Aug 23 08:38:04 2013 No.5986238 >>5985778 I know the rigorous proof you're talking about, it's the one I use whenever I need a proof of that equality, but which part of that guy's proof isn't rigorous ? Is is the <span class="math">\frac{1}{3} = 0.\bar{3}[/spoiler] part ?

Anonymous Fri Aug 23 08:42:05 2013 No.5986244

>>5986215
okay.... theople here seem to be forgetting that 0.999... is an infinatly long number, meaning that there is no number between 0.999... and 1 and no possible number that can get you from 0.999... to 1. and secondly 1/3 is 0.333... and 0.333x3 is 0.999... now without changing any number in the sum you get a different answer than the one you started with. mathimatically this would not happen if anything we use to calculate number could calculate to an infinate number, but as we are limited too an actuall number, we end up with 0.999... instead of 1, so only whilst using thirds does 0.999...=1

>>	Anonymous Fri Aug 23 20:47:07 2013 No.5987321 Pi is infinite, too, and it doesn't suddenly become a different number.

>>	sage sage Fri Aug 23 21:00:09 2013 No.5987351 >>5984756 Why is it so hard for some people to understand that if you have an infinite amount of 9's and answer in a troll thread, then you are bound to get trolled even harder.

>>	Anonymous Fri Aug 23 21:08:38 2013 No.5987366 >>5984756 fuck off OP people smarter than you have proven this

>>	Anonymous Fri Aug 23 21:21:07 2013 No.5987382 >>5986116 0.9 + 0.1 = 1 0.99 + 0.01 = 1 0.999999 + 0.000001 = 1 so what number do you add to 0.999... to make it equal one? remember 0.000...1 isn't a number in the proper sense.

>>	Anonymous Fri Aug 23 21:26:37 2013 No.5987393 For fucks sake, /sci/ couldn't spot a troll if it sat on them.

>>	Anonymous Fri Aug 23 21:38:38 2013 No.5987416 >>5984808 haha its an april fools joke

>>	Anonymous Fri Aug 23 22:00:07 2013 No.5987437 File: 106 KB, 953x613, 0.999=1.jpg [View same] [iqdb] [saucenao] [google] >>5984756 >Infinitly small number don't exist /thread

Anonymous Fri Aug 23 22:09:09 2013 No.5987449

>>5984756
>why do mathematicians believe that 0.999... = 1

They don't believe that. Clearly they are 2 completely different decimal strings and as such they CAN NOT logically be equal (and no, every single arithmetic 'proof' is only a disproof of decimals forming a field, not equality).

What mathematicians know and can prove is that if you DEFINE an equivalence relations on the set of all infinite decimals that puts all finite nonzero decimals in correspondence with one were the last digit is decremented and an infinite trail of 9s are appended; then that forms the real number system under the usual definition of 0,1,+,*,< on these equivalent classes.

It's by definition. Anyone who says you can prove it is a fool, including your high school math teachers.

>>	Anonymous Fri Aug 23 22:20:38 2013 No.5987463 >>5987449 Uh, wow. I don't think I've ever seen someone try to argue mathematics on the basis of STRING COMPARISONS before. Normally it's taken as given that we're talking about numerical comparisons, within the existing definitions of that number set.

Anonymous Fri Aug 23 22:27:37 2013 No.5987475

>>5987463
>I don't think I've ever seen someone try to argue mathematics on the basis of STRING COMPARISONS before

Take a Mathematical Logic course or read a book on it. (A real one, not some hand waving Philosophy or CS crap)

>Normally it's taken as given that we're talking about numerical comparisons, within the existing definitions of that number set.

You can't say anything numerically until you well define the underlining set and operations on it.

Anonymous Fri Aug 23 22:36:09 2013 No.5987493

>>5987475
>You can't say anything numerically until you well define the underlining set and operations on it.
Sure, but you don't do that every time you try to buy groceries. You do that once in a Uni course, and then assume it for the rest of your life.

>>	Anonymous Fri Aug 23 22:43:38 2013 No.5987504 >>5984769 It is as likely to exist, as an infinite number is likely to exist. Mathematicians work with theoretical numbers all the time, this is a relatively simple one in comparison.

>>	Anonymous Fri Aug 23 22:51:08 2013 No.5987514 >>5987504 That's not how numbers work. Good day.

Anonymous Sat Aug 24 07:28:08 2013 No.5987990
File: 100 KB, 480x480, 1375271333810.png [View same] [iqdb] [saucenao] [google]

>>5985818
>tfw the supremum of the sequence
<span class="math"> \omega [/spoiler]
<span class="math"> \omega^{\omega} [/spoiler]
<span class="math"> \omega^{\omega^{\omega}} [/spoiler]
is countable

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