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1 = 0.99999~

Name: Anonymous 2006-02-27 3:21

Discuss.

Name: Anonymous 2006-03-02 18:51

>>38
gb2yurop education ministry

Name: Anonymous 2006-03-02 18:55

42GET! OHR

Name: Anonymous 2006-03-02 20:20

Is 42.99999~GET = 43GET?

Name: Anonymous 2006-03-03 7:44

1= 0.8

Name: Anonymous 2006-03-04 21:59

It's called a limit
GTFO

Name: Anonymous 2006-03-05 7:19

o.999~ < 1

Name: ☭ !K7nLvWsulk#rq+L5rhwzhe+A7o 2006-03-05 8:28 (sage)

>>30
is a lying troll who doesn't know shit. your calculation is wrong and you know it, if you don't, gb2college math 101

Name: Anonymous 2006-03-05 15:21

>>47
QFT

Name: Anonymous 2006-03-05 22:28

>>47

Then prove it wrong, fuckhead.

Name: Anonymous 2006-03-06 2:41

>>49
He doesn't really need to, kid.

Name: Anonymous 2006-03-06 8:31

You can just see it by contradiction. Suppose 0.999~ is not 1, then you can find a real number strictly greater than 0.999~ and strictly less than 1. But you can't.

Name: Edward 2006-03-06 8:58

It just means that the irrational number k = 0.9999~ is infinitely close to 1. By definition, this means nothing is closer to 1 than k. That doesn't mean k = 1.

You can prove the contrary through induction:
k = lim(n->+∞) ∑(n=1) 9*10^n
Take nmax = 1: k1 = 0.9
Take nmax = 2: k2 = 0.9+x = 0.99 where x=0.09 and x < 1-k1
Take nmax = 3: k3 = 0.99+x = 0.999 where x=0.009 and x < 1-k2.

If you see k as an arithmetic series, for every rank, the number added is always inferior to 1-k(n-1) where k(n-1) is the previous rank. Therefore it will grow infinitely close to 1, without ever reaching it, ever.

>>30 was therefore wrong. He was just playing with the misrepresentation that (0.99999~ * 10) - 9 is still 0.9999~, which is a circular proof.

>>47 is therefore correct, but should have provided us with the above truth instead of saging.

Good, you all have it now, you can all let the thread die.

Name: Anonymous 2006-03-06 9:08

>>52
haha oh wow, stop pretending you know shit all about maths.
First of all 0.999~ IS a rational and not an irrational like you claim. If you know anything about decimal expansions then you know that a number is rational iff it has a decimal expansion which is periodic after a certain point.

I am not even going to bother with the rest of the stuff you said as you seem to be a total fuckhead.

SO DON'T LISTEN TO THIS GUY. HE DOESN'T KNOW WHAT THE FUCK HE IS TALKING ABOUT.

Name: Anonymous 2006-03-06 11:01

>>53 has attacked one terminological point in the post, without attacking the rest. He has not even tried to refute the proof. In fact, the point he attacked has nothing to do with the proof as >>52 could well have just posted:

It just means that the irrational number k = 0.9999~ is infinitely close to 1. By definition, this means nothing is closer to 1 than k. That doesn't mean k = 1.
You can prove the contrary through induction:
k = lim(n->+∞) ∑(n=1) 9*10^n
Take nmax = 1: k1 = 0.9
Take nmax = 2: k2 = 0.9+x = 0.99 where x=0.09 and x < 1-k1
Take nmax = 3: k3 = 0.99+x = 0.999 where x=0.009 and x < 1-k2.
If you see k as an arithmetic series, for every rank, the number added is always inferior to 1-k(n-1) where k(n-1) is the previous rank. Therefore it will grow infinitely close to 1, without ever reaching it, ever.

QFT. >>53 doesn't know shit about what he's talking about, and is probably the same person as >>30.

Name: Anonymous 2006-03-06 12:31 (sage)

My God, you people are assholes. I know you're just trolling, but some poor kid might read this and believe you. So let's get something more authoritative:
http://mathworld.wolfram.com/RepeatingDecimal.html
"Numbers such as 0.5 are sometimes regarded as repeating decimals since 0.5=0.5000~=0.4999~."

Name: Anonymous 2006-03-06 12:34

"are sometimes regarded" that sounds very authorative/final.

Name: Anonymous 2006-03-06 12:37

>>55
How the fuck are they trolling? >>30 is just being a bit of an asshole, and being wrong.
>>52 is making a good point. If you guys aren't going to bother coming up to an argument to a common proof by recursion, then you don't really have any say in how unauthorative this thread is.

Name: Anonymous 2006-03-06 12:47 (sage)

>>56
Welcome to English. The claim after 'since' is completely independent of that.

>>57
>>52 is too retarded to understand limits apparently.

Seriously, I'm not going to waste my time on a bunch of trolls. Here's a couple of people with actual qualifications if you'd care: http://www.newton.dep.anl.gov/askasci/math99/math99167.htm
And of course there's a Wikipedia page you can go and edit if you're so convinced of your correctness: http://en.wikipedia.org/wiki/Proof_that_0.999..._equals_1

Name: Anonymous 2006-03-06 12:56

>>54
I am not going to take someone who claims 0.999~ is irrational very seriously. It's clear that the guy knows nothing about maths by the usage of his terms. "infinitely close"?? If you can't find a real number between two real numbers then they must be the same. His so called proof relies on "it's true for n=1, it's true for n=2, it's true for n=3, so it must be true for countably infinite summation". I am sorry, but that simply doesn't work that way. By that arguement you would be able to prove countable intersections of open sets is open, but there are plenty of counterexamples to that.

Name: Anonymous 2006-03-06 13:12 (sage)

LOL @ Mathematicians thinking maths is real.
This is all theoretical shit with no grounding in reality.
It's just like philosophy: intellectual masturbation.

Name: Anonymous 2006-03-06 13:20

Theorem: 1=0.999~ in R

Proof: we recall that R defined set of equivalence classes of converging rational sequences in the topological competion of Q with regard to the relation a ~~ b iif lim(n->inf, a) = lim(n->inf, b).

we note that:

0.999~ ~~ lim(n->inf, 1 - (1/10^n)) = lim(n->inf, 1) ~~ 1

therefore 0.999~ = 1 as required.

qed.

Name: Anonymous 2006-03-06 13:56

>>60

Oh right. Ever heard of number theory? The stuff that makes all the transactions on the internet secure? Get your ass out of your head thanks.

Name: Anonymous 2006-03-06 14:10 (sage)

>>62
I wonder why it's called number THEORY then.
KTHXBYE

Name: Anonymous 2006-03-06 14:28

I guess you dismiss the "THEORY of relativity" or other physical and chemical theories. I guess Gravity doesn't exist for you.

Name: Anonymous 2006-03-06 14:50 (sage)

>>64
Just because you have reasonable doubt about the reality of theories doesn't mean they don't exist, or that we can't take a pragmatic stance on them.
Go back to epistemology 101 motherfucker.

Name: Anonymous 2006-03-06 21:49

>>65
oh ok, so you doubt gravity. fine.

Name: Anonymous 2006-03-06 21:57

Nerd fight, nerd fight!

Name: tadchem 2006-03-07 3:55

1 = 9/9 = 9*(1/9) = 9*(0.11111~) = 0.99999~

QED

Name: Anonymous 2006-03-09 18:17

>>68
something is subtly wrong with this proof (albeit the result 1=.999~ is right) but I just can't figure out what

Name: Anonymous 2006-03-09 20:57

kaka poopoo peepee butt ass lesbian

Name: Anonymous 2006-03-09 21:15

>>69

Perhaps this part: 9/9 = 9*(1/9)

Name: Anonymous 2006-03-09 22:28 (sage)

or:
9*(0.11111~) = 0.99999~

where one assumes you can work with digits separately even if there are infinitely many of them

Name: Anonymous 2006-03-10 2:31

>>71
What's wrong with that part?  Nine ninths makes a whole, last I checked.

Name: Anonymous 2006-03-10 12:03

>>73

The proof is circular.

0.999~ = 9(1/9)=9(0.111~)=0.999~

Name: Anonymous 2006-03-10 13:35 (sage)

>>74
lol

Name: Anonymous 2006-03-10 15:34

i'm a mathamagician

Name: Anonymous 2006-03-10 16:58

>>74
QFT.

Name: Anonymous 2006-03-10 18:30

>>74

It's not circular, it just relies on the fact that 0.111~ = 1/9.

Which can be shown in the exact same way as I proved 1 = 0.999~ in >>30.

Name: Assomatic 2006-03-16 0:14

It's a false question because 0.9999... never occurs from division of any two integers, and therefore is a decimal representation of a fraction that does not exist.  (You could get 0.9999.... from 9/9 if you fuck up the first step of long division, and pretend that there are zero nines in 9.)  You have to bullshit about rational numbers having to equal a limit, or pretend that you start with 1 and infinitely partition it in ever smaller parts in order to compensate for the fuckup.

Name: Anonymous 2006-03-16 19:53

>>79
But 0.3333333~ does happen and it equal 0.4
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