Disclaimer - I am no mathematician, I didn't even do A-level
It's just a theoretical thing isn't it? If there are infinite 9s then the difference between 0.99999 etc and 1 is infinitely small, which is sort of impossible but must work theoretically otherwise you'd just write 1 instead. In practice it probably might as well be the same though. I'm guessing.
In any practical measure then they are the same. Grace is right though.
no matter how matter nines you add it will still be a different number
edit: I think the argument is that if 0.333 recurring is 1/3 and 1/3 x 3 = 1 then 0.333' x 3 = 1
But recurring numbers are an approximation they are not actual numbers so we cannot add or subtract them without limiting the number of decimal places so if we add them then they must stop before infinity and therefore the will add up to less than one.
This is why real mathematicians don't use decimal points.
Does anyone ever wonder why Sam Beckett never spent more time in front of the mirror when he found himslef transported into the body of an attractive lady?
He would have if someone had come up with the late-night concept before. Still credit where credit's due to Hollyoaks for consistent innovation.
At first I said "NO" - cos y'know, theoretically 0.999999... will always be the number closest to 1 but not quite 1.
But as I was reading on the other forum I got it off, the mathematicians on it seemed to largely be in consensus that they are in fact the same thing
because 0.999.... is the same as the sequence 9/10+9/100+9/1000......and so on
and the sum of this infinite series = 1
They're equal.Apart from a mathematical proof, here's another way to understand it: Take any number between 0 and 1. No matter how close you get, 0.9999~ is greater than that number. It cannot, however, be greater than 1.
If there is no number less than 1 but greater than 0.9999~, and 0.9999~ is no greater than 1, then 0.9999~ must equal 1.
because 0.999.... is the same as the sequence 9/10+9/100+9/1000......and so on
and the sum of this infinite series = 1
This is definitely not a proof. the sum of the infinite series is 0.999'
Apart from a mathematical proof, here's another way to understand it: Take any number between 0 and 1. No matter how close you get, 0.9999~ is greater than that number. It cannot, however, be greater than 1.If there is no number less than 1 but greater than 0.9999~, and 0.9999~ is no greater than 1, then 0.9999~ must equal 1
well that doesn't mean anything. There is no integer between 9 and 10, doesn't make them the same. I see the point but this seems more like one of those logic puzzles than a proof.
Infinity always fucked my head up.
BBC Open University did a show called "Hotel Hilbert" all about infinity and remember sitting up watching it when I was about 17, and doing a-level maths and getting completely baffled but dead interested at the same time and went in and asked my teacher about it.
Also, Radio 4 In Our Time done a show on infinity, and on the number zero
Quote:
because 0.999.... is the same as the sequence 9/10+9/100+9/1000......and so on
and the sum of this infinite series = 1This is definitely not a proof. the sum of the infinite series is 0.999'
No this is a proof from what I remember about infinite series - look up infinite series
Quote:
Apart from a mathematical proof, here's another way to understand it: Take any number between 0 and 1. No matter how close you get, 0.9999~ is greater than that number. It cannot, however, be greater than 1.If there is no number less than 1 but greater than 0.9999~, and 0.9999~ is no greater than 1, then 0.9999~ must equal 1
well that doesn't mean anything. There is no integer between 9 and 10, doesn't make them the same. I see the point but this seems more like one of those logic puzzles than a proof.
I kinda agreed with this bit cos I thought it first but you've imposed your own limit by designating that it must be an integer here so that doesn't disprove the guy's point at all. It's completely arbitrary to demand that it must be an integer. In the case of a recurring decimal, it is at the point of infinity that the value becomes the limit - in the case of 0.9999... ,that limit is 1. Otherwise the recurring decimal has no sensible meaning.
Take away the decimal point though and deal in single units. It's meaningless, it would effectively be attempting to say that because there is nothing greater than 1 but less than 2, they must be the same thing.
The inability to find a dividing digit has nothing to do with it because they are defined from the outset as different numbers. There is no end point at which the difference becomes null and void, the difference simply continues to become smaller, defined inherently as difference, for ever. That is the nature of inifinity. It is only within the limited boundary of the human mind that the two things ever become indivisible.
I got a C at GCSE though, so I'm probly talking bollocks.
(edited)
MJ wrote:
There is no difference between having to work for 7.999' hrs and having to work for 8 hrs. Everything else follows from this experienced truth.
If you had to clock off using an atomic clock you'd be waiting a long time to go home - it does sometimes feel like I've been at worik for infinity, but I guess it's all relative. Relativity, now there's an answer 
At first I said "NO" - cos y'know, theoretically 0.999999... will always be the number closest to 1 but not quite 1.But as I was reading on the other forum I got it off, the mathematicians on it seemed to largely be in consensus that they are in fact the same thing
because 0.999.... is the same as the sequence 9/10+9/100+9/1000......and so on
and the sum of this infinite series = 1dude on other forum wrote:
They're equal.Apart from a mathematical proof, here's another way to understand it: Take any number between 0 and 1. No matter how close you get, 0.9999~ is greater than that number. It cannot, however, be greater than 1.
If there is no number less than 1 but greater than 0.9999~, and 0.9999~ is no greater than 1, then 0.9999~ must equal 1.
No, 1.99999~ will never be 1, it doesn't ever reach 1, it goes on to infinity without reaching 1. Even if there is no number less than 1 but greater than 0.9999~ of course a lower closer number will be lower than 0.9999~ no matter how close it gets to that number, eg 0.8999~ will never be 0.9999~ the same as 0.9999~ will never equal 1, let alone ever be greater than it.
This is however a great example of how decimal maths sorta disappears up its own arse. Anyone remember the hypothetical 3 people give so many quid in to the pints, the pints cost x, they should all get the same change but the total change is a quid short of the fraction of the change each should get btw?
An infinite series can tend towards a number without ever reaching it.
for example n + (n/2) + (n/4) + (n/8) etc
would tend towards a number but never reach it, it n were 1 then it would tend towards 2 but as it would only ever cover half the difference between the current term and the next term it would never reach it.
In the same way in this sequence it covers 9/10 of the difference between the two numbers.
apparently I'm wrong I don't like the proofs I've read so far though.
on one hand 0.999999 infinitely recurring can be understood to be an infinitely decreasing gap towards 1 but then where does that leave us in relation to 1 divided by 3, that gives us 0.33333 infinitely recurring are we going to argue that in the division something get's lost from the 1?
To reach 1 from 0.9999999~ infinite 9's one would have to make a quantum leap, i.e. make the smallest possible change in a sytem to create something new. Therefore I think Sam Beckett would argue that there's a shed-load of difference.
I agree with yer first point. (as much as i understand these things which is pretty minimal. )Quantum theory excites me!
And man i loved that prog - thought the one when he leapt into the body of the rape victim was pretty good tbh. And the KKK two-parter - pretty chilling. Course some eps were weaker than others.
on one hand 0.999999 infinitely recurring can be understood to be an infinitely decreasing gap towards 1 but then where does that leave us in relation to 1 divided by 3, that gives us 0.33333 infinitely recurring are we going to argue that in the division something get's lost from the 1?
like an ontological excess or something? a gap or lack of some sorts? 
More unrest in China following further layoffs in the industrial heartland.
The following is an account of the uprising in Kurdistan in 199, which buries the lies of the western media which presented this proletarian uprising as the work of nationalist parties in the north or Shi'ite religious fanatics in the south.
Actress Elizabeth Hurley was fined £70,000 by her union for scabbing on a five month Screen Actors Guild (SAG) strike.
Well, this was on some other board and I thought yis might like a go if you're skiving like me. I'm no mathematician, I got a D in a-level.
Do you think 0.9999999~ infinite 9's is exactly equal to 1?