Poll: Does 0.99 Recurring = 1

AlphaNumeric · 31 Oct 2004 at 19:54

Originally posted by VDO
So tell us what you need to add. What number is between 0.9r and 1?

True. If 0.9r < 1, then there exists a number between them, (0.9r + 1)/2 say. But if 0.9r is the "closest number to 1" then (0.9r+1)/2 is 0.9r isn't it?

(0.9r+1)/2 = 0.9r
0.9r + 1 = 2*0.9r
Take 0.9r from both sides
1 = 0.9r

Hence if you asume 0.9r is the closest number to 1, you still prove it is infact 1

Or you don't accept the basic rules of algebra, and everything you've ever learn in maths is incorrect.

Jokester · 31 Oct 2004 at 19:55

Originally posted by Caerdydd
So just out of curiosity, and this might have been covered earlier...

What is 0.9r + 0.0r1 ?

or 1 - 0.0r1 ?

Yes it has been covered and no it doesn't equal anything becuase you can't stick a number on the end of an infinitely recurring number as it doesn't have an end.

Jokester

memphisto · 31 Oct 2004 at 19:57

Originally posted by sid
I agree

0.0r1 makes no sense

that would be saying that after the decimal point, there are an infinte amount of zeros and then 1 after that. If the number of zeros never ends you cannot put a 1 after that. does anybody understand that??

sid

so there are an infinite number of 9's after the 0. then yeah

so thats still infinetly smaller than 1

Caerdydd · 31 Oct 2004 at 19:57

I'd never thought of it that way

VDO · 31 Oct 2004 at 19:57

Originally posted by Xenoxide
Once again, they may be so infinitely close that you can discard the diference and call it (For arguments sake) the same, but they never will be, no matter how many formulas you can think up say it is so.

Have you bothered to read the numerous proofs people have posted at all? They are not theories. They are not hypothetical formulas. They are proofs.

starscream · 31 Oct 2004 at 19:57

When I first saw the other thread on this, I instantly thought, no it doesnt, for every 9 you add to it, it gets closer to 1 but will never actually equal 1. Having read some of the proof posted in here, I now can see that it does. I did A-Level maths but no further than that so when you are given proof by people with far more knowledge on the subject you than you, you should accept it with an open mind. If you read both sides of the argument its clear that the people that agree are generally the ones with the best knowledge of the subject. I think most people that say 0.99r isn't equal to 1 have never thought or studied this but are making a snap judgement about it. Then when they are given proof that they were wrong they will use the philosophy argument which to be honest can be applied to any subject in the world, rather than back down (this is an internet forum after all

)

AlphaNumeric · 31 Oct 2004 at 19:59

Originally posted by Xenoxide
A recurring number isn't a number since a number has to be finite, whereas a recurring number is infinite.

1/3is 0.3r. Is 1/3 infinite? Last time I checked 1/3 was between 0 and 1, so unless someone completely changed the ordering of The Reals while I wasn't in lectures, 1/3 isn't infinite, but is recurring.

If you've some mindblowing contradication to that, then fire away, I'm all ears......

memphisto · 31 Oct 2004 at 19:59

Originally posted by VDO
So tell us what you need to add. What number is between 0.9r and 1?

0.0r1

VDO · 31 Oct 2004 at 20:00

Originally posted by memphisto
so there are an infinite number of 9's after the 0. then yeah

so thats still infinetly smaller than 1

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?

Xenoxide · 31 Oct 2004 at 20:02

Originally posted by VDO
Have you bothered to read the numerous proofs people have posted at all? They are not theories. They are not hypothetical formulas. They are proofs.

Yes I have read all the proofs blah blah blah. Whatever they say it is not so. Speaking of which, have you bothered to read any of my posts or are you one of those people that think that maths is always right?

Lets think of it a diferent way.

0.9r is 0.9 with an "infinite" number of 9's on the end. Since it is an "infinite" number, can it actually be counted? So how do you know it doesn't end?

Just like space is infinite, eh?

Sigh, yet another endless topic of debate I've managed to get myself involved in.

AlphaNumeric · 31 Oct 2004 at 20:02

Originally posted by memphisto
o.0r1

Is 0.0r1 the closest number to zero you can get?

What about (0.0r1 + 0)/2 ? The average of 0.0r1 and 0. Obviously thats between 0.0r1 and 0, but 0.0r1 is the closest to zero possible.

(0.0r1+0)/2 = 0.0r1

0.0r1 = 2*0.0r1
Take 0.0r1 from both sides
0.0r1 = 0

Satisfied? If 0.0r1 isn't the closest number to zero, what is? After all how can you get smaller than infinite zeros and then a 1?

AlphaNumeric · 31 Oct 2004 at 20:03

Originally posted by Xenoxide
0.9r is 0.9 with an "infinite" number of 9's on the end. Since it is an "infinite" number, can it actually be counted? So how do you know it doesn't end?

Is 1/3 finite? Is 1/3 between 0 and 1? Its got an infinite number of 3s in it, but its finite.

See your error. You seem another person who doesn't understand proofs and just palms them off due to not understanding them

PS Yes, 1,2,3,4,5,6........N, N+1,.......34N+45, 34N+46,..... all the way to infinity is countable

Google "Cardinality, Countability" and you'll see

memphisto · 31 Oct 2004 at 20:04

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?

you mathmaticians are the ones that came up with algebra and all the symbols

we all know what i mean by

0.0r1

it may not have coem from the greatest criminal minds of our times but still I think it just about sums up what that little bit extra needed to get to 1 will be.

AlphaNumeric · 31 Oct 2004 at 20:05

Originally posted by memphisto
it may not have coem from the greatest criminal minds of our times but still I think it just about sums up what that little bit extra needed to get to 1 will be.

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

nige · 31 Oct 2004 at 20:06

If you consider ‘infinity’, the concept is incomprehensible – a number that is infinitely big, so much so it cannot begin to be comprehended. Even the longest number you could possible concoct would be a mere fraction to infinity – you can never reach it. There is no upper cap on numbers, however there is effectively a lower one (negative numbers aside); 0. You can’t get any smaller than zero. Because the gap between 0.99r and 1 (a concept, but that’s not the argument I’m playing with here

), is infinitely small, it is for all intents and purposes, 0. Therefore, there is no gap between 0.99r and 1; they are equal. Although there is issue with it being an infinitely smaller gap, so can always get smaller, this gap is so small it too cannot be comprehended, thus it is basically zero.

Xenoxide · 31 Oct 2004 at 20:06

Originally posted by AlphaNumeric
Is 1/3 finite? Is 1/3 between 0 and 1? Its got an infinite number of 3s in it, but its finite.

See your error. You seem another person who doesn't understand proofs and just palms them off due to not understanding them

PS Yes, 1,2,3,4,5,6........N, N+1,.......34N+45, 34N+46,..... all the way to infinity is countable Google "Cardinality, Countability" and you'll see

Honestly, I understand the "proofs", but I disagree with them. Mathematically speaking and physically speaking are two diferent things, and all the "proofs" here hinge on mathematics.

VDO · 31 Oct 2004 at 20:06

Originally posted by Xenoxide
Yes I have read all the proofs blah blah blah. Whatever they say it is not so. Speaking of which, have you bothered to read any of my posts or are you one of those people that think that maths is always right?

"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.

Lets think of it a diferent way.

0.9r is 0.9 with an "infinite" number of 9's on the end. Since it is an "infinite" number, can it actually be counted? So how do you know it doesn't end?

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

Just like space is infinite, eh?

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

sid · 31 Oct 2004 at 20:07

Originally posted by memphisto
0.0r1

~

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.

AlphaNumeric · 31 Oct 2004 at 20:07

Originally posted by Xenoxide
Mathematically speaking and physically speaking are two diferent things, and all the "proofs" here hinge on mathematics.

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?

Xenoxide · 31 Oct 2004 at 20:07

Originally posted by nige
If you consider ‘infinity’, the concept is incomprehensible – a number that is infinitely big, so much so it cannot begin to be comprehended. Even the longest number you could possible concoct would be a mere fraction to infinity – you can never reach it. There is no upper cap on numbers, however there is effectively a lower one (negative numbers aside); 0. You can’t get any smaller than zero. Because the gap between 0.99r and 1 (a concept, but that’s not the argument I’m playing with here ), is infinitely small, it is for all intents and purposes, 0. Therefore, there is no gap between 0.99r and 1; they are equal. Although there is issue with it being an infinitely smaller gap, so can always get smaller, this gap is so small it too cannot be comprehended, thus it is basically zero.

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.