Poll: Does 0.99 Recurring = 1

Does 0.99 Recurring = 1

  • Yes

    Votes: 225 42.5%

  • No

    Votes: 304 57.5%
  • Total voters
    529
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Originally posted by sid
does that include zero as well. ??
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This is wandering into some complex stuff. With things like this you require limits, possibly the complex plane, integrals and things I probably should know but don't.

Its like 0! = 1. People don't get that because they think 2! = 2.1, but how can that make sense for 0!. You define 0! using the Gamma function since G(n) = (n-1)!, and G(1) = 1. This is in a similar vain. Unfortunatey I tend to avoid these things, so can't offer too much solid maths for this one.
Originally posted by sid
Even for a cambridge maths student, you seem to know helleva lot more than anybody else here?
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Given there arent many other maths students here, that'd be vaguely expected wouldn't it? ;)

Anyway, the function is just the derivative of x^x written in an integrable and well defined (for the domain) way :)
 
I've never come across this before, its very clever though

It sounds like due to flaws in mathematics 0.99r can equal 1

Its obviously a flaw in mathematics though, because in reality 0.99r is less than 1

Vote: no
 
Originally posted by Caerdydd
It sounds like due to flaws in mathematics 0.99r can equal 1

Its obviously a flaw in mathematics though, because in reality 0.99r is less than 1
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Run away. Run away very fast before Alpha gets you :p

It's not a flaw in mathematics. It is, if you like, a flaw in how mathematics translates to the real world. In the real world, the only problem is that you can't have an infinite number of 9's, so all the fancy equations fall flat on their faces because, for all its space-shuttle-launching capability, your calculator cannot cope with the number 0.9r. But in mathematics, you can take as a given that there are an infinite number of 9's after that decimal point, so everything works out.
 
No matter how close 0.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 is to 1, it will never be 1, unless you add that last little bit onto it to make it 1.

However, in reality, you could say that it is so close to 1 that it should be 1. It's like walking into a shop and taking something worth £4.99 to the till and you take out your wallet and you only have £4.98. Sometimes they let you off, sometimes they dont.

To be honest, it really depends on the situation.
 
^Actually, it's nothing like shopping.

If you read through the proofs scattered liberally across all the threads this argument has popped up in, you'll see that mathematically, 0.9r is most definitely equal to 1.
 
Those aren't proofs, those are theories, and theories that I disagree with.

1 is a finite number. It's 1. It's nothing else. But 0.9r can be 0.99 or 0.999 or 0.9999. They may be VERY VERY VERY close but they will never be the exact same.

An infinite number is not the same as a finite number.
 
Originally posted by Xenoxide
Those aren't proofs, those are theories, and theories that I disagree with.

1 is a finite number. It's 1. It's nothing else. But 0.9r can be 0.99 or 0.999 or 0.9999. They may be VERY VERY VERY close but they will never be the exact same.

An infinite number is not the same as a finite number.
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They most certainly are proofs. Proofs that have come from some of the greatest minds ever to have lived.

0.9r can not be 0.99 or 0.999 or 0.9999. I suspect you also misunerstand the concept of infinity. I won't repeat the proofs, you can see them for yourself, bit I ask you, is there a number between 0.9r and 1?

Incidentally, 0.9r is not an infinite number ;)
 
Originally posted by Xenoxide
0.9r can be 0.99 or 0.999 or 0.9999. They may be VERY VERY VERY close but they will never be the exact same.
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No. 0.9r is not 0.9, or 0.99, or anything else. 0.9r is 0.99999 forever and ever and ever and ever and ever and ever.....9999999 and then some.

The 9's never end.

0.9r = 1
 
Yes, but no matter how many 0.9999's... there are, it will never be EXACTLY one. You always need to add that little bit on to make it exactly. All these so called proofs use mathematics and formulas to "prove" something, but this is one of those cases where I think it's wrong. And you can say it's right all you want, but in reality, it isn't.
 
Originally posted by Xenoxide
Yes, but no matter how many 0.9999's... there are, it will never be EXACTLY one. You always need to add that little bit on to make it exactly. All these so called proofs use mathematics and formulas to "prove" something, but this is one of those cases where I think it's wrong. And you can say it's right all you want, but in reality, it isn't.
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So tell us what you need to add. What number is between 0.9r and 1?
 
It does make sense in my head.

Mathematically all the sums are correct and 0.99r can equal 1.

But there is obviously a flaw somewhere along the line, because 0.99r is (or atleast should be) a smaller number than 1.
 
Originally posted by Xenoxide
Yes, but no matter how many 0.9999's... there are, it will never be EXACTLY one. You always need to add that little bit on to make it exactly. All these so called proofs use mathematics and formulas to "prove" something, but this is one of those cases where I think it's wrong. And you can say it's right all you want, but in reality, it isn't.
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OK, I challenge you (or anyone) to find a positive real number that can be added to 0.9r to make 1.

If you like I can write a proof to show that no matter what number you choose the result will be greater than 1.
 
Originally posted by Xenoxide
but this is one of those cases where I think it's wrong. And you can say it's right all you want, but in reality, it isn't.
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A view you are perfectly welcome to, provided you back it up. Do you have any proof other than "I think its wrong". Saying "It never actually reaches it" doesn't cut it, because it maths, it does reach it. Feel free to post a counter-proof (theres an oxymoron if ever I heard one).
 
Originally posted by VDO
So tell us what you need to add. What number is between 0.9r and 1?
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Honestly, I see where you are coming from, but it's just not so.

Since it's a recurring number there is no way to tell what you need to add to make it that, but there will always be something, no matter how small.

Take for example a piece of string which is 100,000,000 miles long. If you divide it by three you get 33,333,333r miles. But if you multiply it by three you get 99,999,999r miles. If you took a 100,000,000 mile long piece of string, and put three 33,333,333r mile long pieces of string parallel to it, they may be very very close in length but never the same.

A recurring number isn't a number since a number has to be finite, whereas a recurring number is infinite. You could say that to divide 100,000,000 you could make it 2x 33,333,333 and 1x 33,333,334 and discard the diference as negligible, but they WILL NEVER be the same.

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.

Mathematically speaking they may be the same. But I once read a topic on this subject, and a reply by a professor stated that "Maths is not always about right or wrong. Usually it is about definently maybe."
 
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Originally posted by Caerdydd
So just out of curiosity, and this might have been covered earlier...

What is 0.9r + 0.0r1 ?
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There is no such thing as 0.0r1

There are an infinite number of zeros, so there can't be a one.

And yes, this has in fact been covered earlier.
 
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