Poll: Does 0.99 Recurring = 1

riven · 31 Oct 2004 at 20:08

ok, heres one for alpha, i got my head teacher (phd in logic and extremely good at maths) to explain to me.

If an irrational number ie. pi has no end, then even though it is getting smaller by such a small amount each time, is it not getting infinately large?

Gigi · 31 Oct 2004 at 20:08

Me thinks this will go on forever and ever.

/Gigi

yak.h'cir · 31 Oct 2004 at 20:10

Originally posted by VDO
Indeed. And how do you represent a number "infinitely smaller" than 1?

The only way I can think of is 1-(1/infinity). How do you write 1/infinity? 0.0r1?

Now, where have I seen this before?

I believe 1/infinity is either taken to be 0, or as an infinitesimal...

sid · 31 Oct 2004 at 20:10

Originally posted by VDO
"Whatever they say it is not so"?
Strikes me as just mildly arrogant. How do you demonstrate this? You most certainly haven't done so in your posts - which I have indeed read, and responded to.

I don't think you noticed when I mentioned that "mathematically speaking" 0.9r=1
I don't think that math is "always right", but when it is math problems we're talking about, then yes, math is indeed the only way to go about things.

Because, for Christ's sake, that's how it's bloody well defined.

As I said, mathematics does not always translate well to the real world, so "space" has nothing to do with it.

I dont think he understands the whole concept of inifinity in maths. I cant say that I understand every detail of it.

Asking to quantify infinite is contradiction itself. People here seem to struggling badly to get a grasp of this.

Jokester · 31 Oct 2004 at 20:10

Originally posted by Xenoxide
That's what I'm saying. "For all intents and purposes". "For arguments sake", whatever, the number between them cannot be counted, but there will always be something.

Despite what over members have said there is no difference between 0.9r and 1 such that:-

1 - 0.9r is exactly 0 with no infinitely small bit left over.

Jokester

Xenoxide · 31 Oct 2004 at 20:11

Originally posted by AlphaNumeric
Last time I checked infinity was a mathematical construcct, 0.9r was a mathematical construct, so why shoudln't the proof be mathematical? What should it be written in? Finnish?

Ok, tell me this.

Is 9 equal to 10?

Is 0.9 equal to 1?

Is 0.99 equal to 1?

0.9r is just 0.99 with more 9's on the end. 9 IS NOT 1.

No matter how small there will always be something. It just cannot be described.

The guy who asked me to tell him "what do you add onto 0.9r to make 1". I honestly cannot answer, but there will always be something, no matter how small, no matter how un-countable.

Does this not make you think that perhaps mathematics are flawed? Since 0.9r is infinite and can be described as "0.9r", should there not be something to describe the very small part in between?

memphisto · 31 Oct 2004 at 20:11

Originally posted by AlphaNumeric
See my last but 2 post, it shows 0.0r1 (the difference) is zero

yes but your using mathmatics to prove the point, this is more philosophical than mathmatics.

The thing is and this isnt having a go at mathmaticians but you can come up with mathmatical equations for which side yer toast is going to land on, I think I read the other day that some mathmaticians have come up with a formula for sods law.

Basically what I am saying is by using maths you can use algebra and equations to prove anything you want, from the weather cycle, to the time its going to take me to tie my shoelaces in the morning.

So you can easily come up with an equation to show 0.99r = 1 even if it doesnt.

Hell I bet you could probably come up with an equation that says 3 =1 given enough time and resources

AlphaNumeric · 31 Oct 2004 at 20:12

Originally posted by riven
If an irrational number ie. pi has no end, then even though it is getting smaller by such a small amount each time, is it not getting infinately large?

The rate of decreasing in size of each "extra decimal place" is sufficently fast that it tends to a limit.

1/n summed for 1/1 + 1/2 + 1/3 + 1/4 + etc goes to infinity. Its rate of decresion is too small.

1/n^2 summed for 1/1 + 1/4 + 1/9 + 1/16 tends to a limit (pi^2/6 as it happens) because 1/n^2 gets really small really quick.

There's various fields of maths for this purpose. Us the Gauss formula

x + X/10 + X/100 + X/1000 + ....... = X(1-[0.1]^n)/(1-[0.1])

To work out that no matter the choice of X and n (except X = infinity, but thats obvious) you always get a limit.

Let x = 9, so you get 9.99999....... > pi = 3.1415.....

9 + 0.9 + 0.09 + ...... = 10

Hence 10 > pi, even though its an infinite sum

memphisto · 31 Oct 2004 at 20:12

Originally posted by sid
~

You are being plain daft here now

I posted why what your saying makes no sense

you are saying that that there are infinite number of 0.000......then....00001 arent you

Well listen to this

The number of zeros doesnt end. ever. never.

so you cannot physically have that 1 at the end as you.

that is the truth. You cannot argue your case mathematically so dont try. Alpha will eat you by the looks of things.

I'm not trying to argue the case mathmatically, and as you say there may never be an end to the 0 in 0.0r1

the same as there is never an end to the 9's in 0.9r but that still means its 0.0r1 away from being 1.

Xenoxide · 31 Oct 2004 at 20:14

Originally posted by VDO
"Whatever they say it is not so"?
Strikes me as just mildly arrogant. How do you demonstrate this? You most certainly haven't done so in your posts - which I have indeed read, and responded to.

I don't think you noticed when I mentioned that "mathematically speaking" 0.9r=1
I don't think that math is "always right", but when it is math problems we're talking about, then yes, math is indeed the only way to go about things.

Because, for Christ's sake, that's how it's bloody well defined.

As I said, mathematics does not always translate well to the real world, so "space" has nothing to do with it.

"Maths does not always translate well to the real world".

Then in my view, maths are irrelevant.

PS: Thanks for your "mildly arrogant" comment, I was thinking the same about you but didnt want to say it for fear of sounding "mildly arrogant".

PPS: "How do you demonstrate this? You most certainly haven't done so in your posts". Because there is no way to describe the infinitely small number that goes inbetween the infinitely large number of 0.9r.

You can comprehend that something is infinitely large but you cannot comprehend infinitely small? Eh? I find this "mildly arrogant".

AlphaNumeric · 31 Oct 2004 at 20:14

Originally posted by memphisto
Hell I bet you could probably come up with an equation that says 3 =1 given enough time and resources

Thats the point, we can't. If I do a proof to something and get 1 = 2, I scrunch up the paper, chuck it in the bin and start again. Why? Because its known to be false.

All these proofs seem complex and seem like they could be used to prove anything, but if we show 1 = 2, which we know to be false, we know we can't use that "proof" because its a lie.

I challenge anyone to use 0.9r = 1 to prove 1 = 2 (and I don't mean using the "divide by x-y = 0 trick).

VDO · 31 Oct 2004 at 20:14

Originally posted by yak.h'cir
I believe 1/infinity is either taken to be 0, or as an infinitesimal...

Yep

That's exactly what I'm getting at!

riven · 31 Oct 2004 at 20:15

Originally posted by AlphaNumeric
The rate of decreasing in size of each "extra decimal place" is sufficently fast that it tends to a limit.

1/n summed for 1/1 + 1/2 + 1/3 + 1/4 + etc goes to infinity. Its rate of decresion is too small.

1/n^2 summed for 1/1 + 1/4 + 1/9 + 1/16 tends to a limit (pi^2/6 as it happens) because 1/n^2 gets really small really quick.

There's various fields of maths for this purpose. Us the Gauss formula

x + X/10 + X/100 + X/1000 + ....... = X(1-[0.1]^n)/(1-[0.1])

To work out that no matter the choice of X and n (except X = infinity, but thats obvious) you always get a limit.

Let x = 9, so you get 9.99999....... > pi = 3.1415.....

9 + 0.9 + 0.09 + ...... = 10

Hence 10 > pi, even though its an infinite sum

nice one, pretty much how he explained it. Also did you know greek mathmaticians where afraid by the concept of infinity and refused to believe it existed. There was a long article about infinity in new scientist a few months back.

sniffy · 31 Oct 2004 at 20:17

i can't believe people said yes. ITS SIMPLE MATH.

0.99999999999999999999 (This goes on until every single PC in the world with a connection has filled up its text documents with 999's) will never, ever turn into 1.

Common sense? You take away the decimal point and it's still 0. I really dont know how people can argue with that, strange....

AlphaNumeric · 31 Oct 2004 at 20:18

Originally posted by Xenoxide
Then in my view, maths are irrelevant.

Guess who designed the electronic pathways to your PC. Guess who came up with the equations to describe electron behaviour. Guess who made your GPS system work. Guess who came up with the idea behind your monitor. Mathematicians.

If maths had no real world basis you wouldn't have a PC to type on, since no one would be able to describe electronics

Originally posted by riven
where afraid by the concept of infinity and refused to believe it existed.

They burned Pythagoras's school of maths to the ground, killing most of its members out of fear of them.

memphisto · 31 Oct 2004 at 20:18

Originally posted by AlphaNumeric
Thats the point, we can't. If I do a proof to something and get 1 = 2, I scrunch up the paper, chuck it in the bin and start again. Why? Because its known to be false.

All these proofs seem complex and seem like they could be used to prove anything, but if we show 1 = 2, which we know to be false, we know we can't use that "proof" because its a lie.

I challenge anyone to use 0.9r = 1 to prove 1 = 2 (and I don't mean using the "divide by x-y = 0 trick).

and so we get to the hub of the matter, you can use equations to proove anything you want, but if you know it to be false then you throw it away. Therefore in a mathmaticians opinion 1 cannot = 2 so all proofs are thrown in the bin.

however in your opinions 0.9r can = 1 therefore lets all get behind it and preach that it is so. why didnt the bloke who thought 0.99r = 1 just have scrunched up his bit of paper and gone nah its a lie 0.9r will always be infinetly smaller than 1

AlphaNumeric · 31 Oct 2004 at 20:19

Originally posted by sniffy
Common sense?

If you sat through my 1st year Groups lectures, you'd know that common sense gets checked at the door in maths.

Originally posted by sniffy
ITS SIMPLE MATH.

Yes it is. 0.9r = 1. If its not, use it to prove 1>1. I'll be waiting

VDO · 31 Oct 2004 at 20:20

Originally posted by Xenoxide
Ok, tell me this.

Is 9 equal to 10?

No

Is 0.9 equal to 1?

No

Is 0.99 equal to 1?

No

0.9r is just 0.99 with more 9's on the end. 9 IS NOT 1.

0.9r is not simply 0.99 with "more" 9's on the end, it is 0.99 with an infinite number of 9's on the end.
And I think most of us would agree with you when you state that "9 is not 1". I certainly never made a claim to the contrary.

No matter how small there will always be something. It just cannot be described.

The guy who asked me to tell him "what do you add onto 0.9r to make 1". I honestly cannot answer, but there will always be something, no matter how small, no matter how un-countable.

That would be me, and yes. It will be what people describe as "0.0r1". Which is a silly concept, for reasons I and others have given.

Does this not make you think that perhaps mathematics are flawed? Since 0.9r is infinite and can be described as "0.9r", should there not be something to describe the very small part in between?

No, it does not make me think mathematics is flawed.
0.9r is not infinite. Where did you get that from?
There is nothing in between 0.9r and 1. That is what we are getting at here. 0.9r is equal to 1, there is nothing in between.

AlphaNumeric · 31 Oct 2004 at 20:21

Originally posted by memphisto
Therefore in a mathmaticians opinion 1 cannot = 2 so all proofs are thrown in the bin.

Actually you show 1>1, not 1=2 (which is possible in certain systems), I just thought that example would be easier for people to follow.

Originally posted by memphisto
however in your opinions 0.9r can = 1 therefore lets all get behind it and preach that it is so. why didnt the bloke who thought 0.99r = 1 just have scrunched up his bit of paper and gone nah its a lie 0.9r will always be infinetly smaller than 1

Okay, prove 1>1 using 0.9r = 1.

yak.h'cir · 31 Oct 2004 at 20:22

Originally posted by Xenoxide
"PPS: "How do you demonstrate this? You most certainly haven't done so in your posts". Because there is no way to describe the infinitely small number that goes inbetween the infinitely large number of 0.9r.".

I believe it has been said before by alpha and others but 0.9r is no where near an infinite number! I'm not really sure if infinity is considered a real number or not but it is best to think of it as a number so large thats is bigger then any number you can make up. i.e. not a number that wheter or not you take to equal 1 or not is definitly not greater then 1 so it will always be a relatively small number!!!