/sci/ - Science & Math

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Anonymous Mon Jan 30 23:57:01 2012 No.4313133 [Reply] [Original]

Discus

>>	Anonymous Mon Jan 30 23:58:12 2012 No.4313140 naw

>>	Anonymous Mon Jan 30 23:58:12 2012 No.4313139 your mother gives good head.

>>	Anonymous Tue Jan 31 00:02:40 2012 No.4313156 1/0=infinity

>>	Anonymous Tue Jan 31 00:03:49 2012 No.4313161 Ever notice how the equal sign is like a bar notation for a bar notation?

>>	Anonymous Tue Jan 31 00:04:56 2012 No.4313163 dsecxdx

>>	Anonymous Tue Jan 31 00:04:56 2012 No.4313166 yes

>>	Anonymous Tue Jan 31 03:35:48 2012 No.4313762 >>4313133 0.3333... = 1/3 0.9999... = 3*1/3=1 there's nothing to discuss, it's true ... but i admit it looks awesome

>>	Anonymous Tue Jan 31 03:36:55 2012 No.4313764 >>4313161 Whoa man, you just like, blew my mind?

>>	resident /sci/ economist !!0CqB7P/574e Tue Jan 31 03:40:19 2012 No.4313770 File: 108 KB, 646x1305, 1321135578822.jpg [View same] [iqdb] [saucenao] [google] >>4313161

>>	Anonymous Tue Jan 31 04:41:32 2012 No.4313849 >>4313762 We had this nonsense so often: 1/3 is NOT 0.333... Please stop this retarded bullshit and fuck off, troll.

>>	resident /sci/ economist !!0CqB7P/574e Tue Jan 31 04:47:12 2012 No.4313853 File: 40 KB, 650x503, 1301592743178.gif [View same] [iqdb] [saucenao] [google] 1 = .9999.... Its the truth.

>>	Anonymous Tue Jan 31 04:48:19 2012 No.4313855 >>4313853 >tripfag >shitposting troll Is it correlation or causation?

Anonymous Tue Jan 31 04:51:43 2012 No.4313857

>>4313133
Argument 1-
It is because that's the convention in the math world at large. If you disagree with the convention, fuck off. This notation is already in common use. It's defined to be the limit of the sum of the cauchy sequence.

Argument 2-
1: 0.999... ought to be a Real Number.
2: Two Real Numbers are distinct iff there's a distinct Real Number between them. (Easily proven.)
3: There is no distinct Real Number between 0.999... and 1.
4: Thus 0.999... = 1.

Argument 3:
Real Numbers are defined as the set of cauchy sequences over rationals (alternatively dedekind cuts). As such, it follows quite readily that a decimal expansion 0 . a_1 a_2 a_3 a_4 ... = lim x->inf of sum i = 1 to x of a_i / 10^i. Thus 0.999... = 1.

resident /sci/ economist !!0CqB7P/574e Tue Jan 31 04:53:59 2012 No.4313859

>>4313857

>2: Two Real Numbers are distinct iff there's a distinct Real Number between them. (Easily proven.)

Could you do that? I would be interesting in seeing it.

I always thought 1 = .9999... because there is an infinitely small distance between the two, and infinitely small means zero.

mathgenius (not trolling) !!Ceavr+zDPUk Tue Jan 31 04:59:40 2012 No.4313865

>come to /sci/
>see this thread

I can't believe you guys are still arguing, after I proved 0.999... and 1 not to be equal some weeks ago.

>>4313853
The truth? You post this like a religious statement to believe in. Mathematics doesn't work this way. Prove it or stfu. No, actually don't even try, you would waste a lot of time trying to prove a false statement. Proofs of them not being equal can be looked up in the archive.

>>4313857
Ad argument 1: Convention is a matter of style, not a proof. The statement discussed here requires a rigorous proof.

Ad argument 2: There are infinte real numbers between 0.999... and 1. For example (1 - 0.999...)/2 is one of them.

Ad argument 3: The sum you posted does not represent 0.999... In fact it cannot, because the limit of your sequence is 1 and not 0.999...

>>	Anonymouse !70ikdWM2E6 Tue Jan 31 05:00:47 2012 No.4313866 Reported for boring and shitty thread.

>>	resident /sci/ economist !!0CqB7P/574e Tue Jan 31 05:01:56 2012 No.4313870 >>4313865 Could you prove it again? I guess you might not care about my interests, but I would appreciate seeing it. >You post this like a religious statement to believe in. Sorry, I didnt mean it to sound that way.

>>	Anonymous Tue Jan 31 05:02:03 2012 No.4313871 >>4313859 http://en.wikipedia.org/wiki/Trichotomy_%28mathematics%29

>>	mathgenius (not trolling) !!Ceavr+zDPUk Tue Jan 31 05:04:20 2012 No.4313874 >>4313870 http://archive.installgentoo.net/sci/thread/4213228#p4213309

Anonymous Tue Jan 31 05:07:44 2012 No.4313880

>>4313865
>Ad argument 1: Convention is a matter of style, not a proof. The statement discussed here requires a rigorous proof.
There can be no such "rigorous proof". It's a matter of notation, and notation is by fiat, aka by convention, aka by definition. The notation:
0.999... (with a bar)
is by definition
lim n->inf of sum i = 1 to n of lim 9/10^i.

It is defined this way because the sequence
s(n) = sum i = 1 to n of lim 9/10^i
aka:
s(1) = 9/10
s(2) = 9/10 + 9/100
s(3) = 9/10 + 9/100 + 9/1000
(etc)
is Cauchy, and it is a sequence of rational numbers, and thus it is a Real Number. Consequently, we can use the rules of the Cauchy construction of Real Numbers to show that it is equal to 0.

Also:
http://en.wikipedia.org/wiki/0.999......

But really, the short answer is: "Because the notation is defined to be the limit of the Cauchy sequence." Any other answer is persuasion, and not formally correct.

resident /sci/ economist !!0CqB7P/574e Tue Jan 31 05:10:51 2012 No.4313884

>>4313874

Tsh! Thats not proof.

There is no distance between .999... and 1. If there is no distance they are the same. Thats the way I see it.

You cant just say

.99 != 1
Therefore .999.. != 1

Because there is a distance between finite and infinite amount of 9s. One has a defined distance from one, that other has an infinitely small distance.

>>	Anonymous Tue Jan 31 05:11:08 2012 No.4313886 >>4313880 is Cauchy, and it is a sequence of rational numbers, and thus it is a Real Number. Consequently, we can use the rules of the Cauchy construction of Real Numbers to show that it is equal to 1. Correction.

mathgenius (not trolling) !!Ceavr+zDPUk Tue Jan 31 05:13:16 2012 No.4313891

>>4313880
>There can be no such "rigorous proof".
Indeed, there can be no proof for a false statement.
>0.999... (with a bar) is by definition lim n->inf of sum i = 1 to n of lim 9/10^i.
Wrong. This is not the definition. Don't change definitions for your needs.
>citing wikipedia
Unreliable source for mathematical proofs. Even more so now after you managed to find wrong and fallacious "proofs" in there.

>>4313884
There is a distance: 1 - 0.999... = 0.000....0001

>>	Anonymous Tue Jan 31 05:14:23 2012 No.4313895 >>4313891 >Wrong. This is not the definition. Don't change definitions for your needs. So, shall I scan my math textbooks that I have lying around?

>>	resident /sci/ economist !!0CqB7P/574e Tue Jan 31 05:16:39 2012 No.4313899 >>4313891 >0.000....0001 After an infinite number of 0s, that does equal 0.

Anonymous Tue Jan 31 05:22:20 2012 No.4313907

>>4313895
Here. Found one online.
http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDF

Theorem 1.1.4 (The Archimedean Property) If X and Y are positive [Real Numbers]; then
n X > Y for some integer n.

Suppose 0.000...0001 is a Real Number.
1 is a Real Number.
Thus, by the theorem, exists integer n so that n * (0.000...0001) > 1.
Except, this is patently false.
Ergo, (0.000...0001) is not a Real Number.

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