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Forums - General - 0.9999.... = 1.0

 

Are you convinced?

Yes 34 58.62%
 
No 20 34.48%
 
not sure 1 1.72%
 
Total:55
Netyaroze on 30 April 2013
drkohler said:
Netyaroze said:

The difference between 0.9999..... and 1 is infinitely small but infinites can never end so 0.9999..... can never really equal 1 its always just almost 1 in theory.

 No. you don't get it. 0.(period)9 is EXACTLY 1

0.(period)9 can be written as a convergent geometrical series which has the mathematical value of 1.


Yes I saw the argument and its correct. Its practically 1. Still there is one thing in nature that reflects that it will never be 1. Eventhough getting arbitrarily close means that they're equal mathematically speaking.

 

Lightspeed can never be reached for objects with mass, you can get arbitrarily close but it will never be lightspeed no matter what you do. So 0.9999..c is c in mathematics but in real life everything becomes nothing if that were to happen. Humans can not understand infinities math breaks down too the more we get to a singularity/infinity.  



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MDMAlliance on 30 April 2013
pezus said:
MDMAlliance said:
There are many reasons why I can say that .999... does not equal 1 and why every proof I've seen does not work.
If 0.999... is equal to 1, you acknowledge that you do not understand infinity because it is a concept, not a number. 0.999 and any number that "approaches" a value but never reaches it is infinite and is not an actual number.
You can always add another 9 to the list, yes. However, it never stops. It keeps going, but it never reaches 1 either.

I can disprove the geometric series argument, the 1/3 and the 9/9's argument. The geometric series argument is disproved by the fact that if you try representing the series visually, you can actually see that there will always be a space that is not taken up with each new set. In just pure math, that space will continue to get smaller and smaller, but will always exist as well.
Now for the 1/3 and 9/9's argument, you would have to redefine the way we count our decimals.
If we only counted to 2 before going to the next place, you can represent 1/3 as 0.1
If we only counted to 8 before going to the next place, you can represent 1/9 as 0.1
then 3/3 = 1 and 9/9 = 1.
With .999... as it is gathered from infinite series, for the first example it would be written as 0.222...
and for the second it would be written as 0.888...
Due to that fact, you can see why those arguments do not work. 0.999... will still be represented as an infinitely continuing decimal, no matter how you put it. Because it represents a concept of something that continually gets closer to 1 and never does.

I don't know how clearly I am presenting this, but I know that 0.999... does not equal 1.
It is also impossible to visualize 0.999... just as it is impossible for you to visualize infinity. It is as good as 1 in that regard, but in the end they are still different things.

You know this when the entire mathematical world disagrees with you? Ok then...

It seems to me like it is you who has a problem with understanding the concept of infinity and not the ones who have put forth proofs. Read what I posted from wikipedia earlier about why some mathematicians believe that believing 0.999... = 1 is so hard for many. 


Since when was wikipedia a reputable source for information on debateable topics?

You probably didn't read or understand what I typed before that statement you bolded.  I understand why mathematicians say 0.999... is equal to 1.  However, I do not agree with the assessment on non-practical grounds.  The argument may be really pointless, as the reason for 0.999 not equaling 1 for me has no real world applications and for it to equal 1 would.  

Either way, 0.999... is not the exact same thing as 1 due to the fact that it is created by something of infinite "additions."  1 is 1, 0.999... is not.  It's the same logic as there's no "biggest number" so therefore infinity isn't the same thing as the "biggest number" because it doesn't exist.



drkohler on 30 April 2013
Netyaroze said:


Yes I saw the argument and its correct. Its practically 1. Still there is one thing in nature that reflects that it will never be 1. Eventhough getting arbitrarily close means that they're equal mathematically speaking.

 

Lightspeed can never be reached for objects with mass, you can get arbitrarily close but it will never be lightspeed no matter what you do. So 0.9999..c is c in mathematics but in real life everything becomes nothing if that were to happen. Humans can not understand infinities math breaks down too the more we get to a singularity/infinity.  

No. Just no. Just because you have to write 9s until you die/run out of pens/out of money/out of paper, 0.(period)9 IS EXACTLY 1. there is no "getting arbitrarily close". Any PARTIAL sum of the geometrical series is getting close to 1, howerver,  0.(period)9 IS EXACTLY 1.

In the case of infinite convergent series, we fully "understand" infinity and math does not "get into a singularity" - this is Star Trek speak, not math speak.



Soleron on 30 April 2013
MDMAlliance said:
...

Either way, 0.999... is not the exact same thing as 1 due to the fact that it is created by something of infinite "additions."  1 is 1, 0.999... is not.  It's the same logic as there's no "biggest number" so therefore infinity isn't the same thing as the "biggest number" because it doesn't exist.

It's not created by infinite additions. It's a fixed object with certain properties. Everything we do to test those properties (addition, multiplication, comparison) shows it is indistinguishable from 1. And the best way of thinking about it is that the number '1' has two valid decimal representations, being 1 and 0.999...



dsgrue3 on 30 April 2013
Soleron said:
dsgrue3 said:
x = 2
x^2 = 4
x = +/- 2

Fuzzy math is fuzzy. This is why it doesn't sit well with me.

I understand it through Pezus' example with fractions, but this isn't an equation. It's just an assertion.

It isn't a proof at all.

Surely you admit -2 != 2?

you're not allowed to multiply or divide equations by x without handling the fact you just added/removed a solution. In this case the second negative solution is an artifact because you multiplied by x. This happens all the time in real physics problems and you can just ignore the other solution. There is a more formal way to deal with it in pure maths but I'm not practiced with it.

Right, but this isn't an equation which is my point. It's a declaration of a variable. There is no equation in the OP or my post which is why this type of "proof" is bunk.



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Netyaroze on 30 April 2013
drkohler said:
Netyaroze said:


Yes I saw the argument and its correct. Its practically 1. Still there is one thing in nature that reflects that it will never be 1. Eventhough getting arbitrarily close means that they're equal mathematically speaking.

 

Lightspeed can never be reached for objects with mass, you can get arbitrarily close but it will never be lightspeed no matter what you do. So 0.9999..c is c in mathematics but in real life everything becomes nothing if that were to happen. Humans can not understand infinities math breaks down too the more we get to a singularity/infinity.  

No. Just no. Just because you have to write 9s until you die/run out of pens/out of money/out of paper, 0.(period)9 IS EXACTLY 1. there is no "getting arbitrarily close". Any PARTIAL sum of the geometrical series is getting close to 1, howerver,  0.(period)9 IS EXACTLY 1.

In the case of infinite convergent series, we fully "understand" infinity and math does not "get into a singularity" - this is Star Trek speak, not math speak.


Yes as I said mathematically speaking you are right. But in reallity its not 1 as I showed that 0.(period)9 c is not c in real life because its impossible to reach. And math can try to describe infinities but there is no real life proof what really happens its a theoretical construct.

 

Or are you telling me the only way to look at it is the mathematical one ? Math could describe the world but at a certain point it makes no sense in real life terms. 

 



MDMAlliance on 30 April 2013
Soleron said:
MDMAlliance said:
...

Either way, 0.999... is not the exact same thing as 1 due to the fact that it is created by something of infinite "additions."  1 is 1, 0.999... is not.  It's the same logic as there's no "biggest number" so therefore infinity isn't the same thing as the "biggest number" because it doesn't exist.

It's not created by infinite additions. It's a fixed object with certain properties. Everything we do to test those properties (addition, multiplication, comparison) shows it is indistinguishable from 1. And the best way of thinking about it is that the number '1' has two valid decimal representations, being 1 and 0.999...


How is 0.999... a fixed object?  Is there some way you're getting 0.999... that I do not know of?  

Are we talking about two different 0.999...'s because I don't think it would be a fixed object.

If we talk about 1/9 * 9 or 1/3 * 3 (or whatever else way people use to get 0.999 and 1 being the same thing), to some extent I agree that those two numbers are representing the same thing.  I do not agree, however, that 0.999... as an infinity is 1. 



dsgrue3 on 30 April 2013
MDMAlliance said:
Soleron said:
MDMAlliance said:
...

Either way, 0.999... is not the exact same thing as 1 due to the fact that it is created by something of infinite "additions."  1 is 1, 0.999... is not.  It's the same logic as there's no "biggest number" so therefore infinity isn't the same thing as the "biggest number" because it doesn't exist.

It's not created by infinite additions. It's a fixed object with certain properties. Everything we do to test those properties (addition, multiplication, comparison) shows it is indistinguishable from 1. And the best way of thinking about it is that the number '1' has two valid decimal representations, being 1 and 0.999...


How is 0.999... a fixed object?  Is there some way you're getting 0.999... that I do not know of?  

Are we talking about two different 0.999...'s because I don't think it would be a fixed object.

If we talk about 1/9 * 9 or 1/3 * 3 (or whatever else way people use to get 0.999 and 1 being the same thing), to some extent I agree that those two numbers are representing the same thing.  I do not agree, however, that 0.999... as an infinity is 1. 

It's fixed in the same way that Pi or E are fixed.



MDMAlliance on 30 April 2013
dsgrue3 said:
MDMAlliance said:


How is 0.999... a fixed object?  Is there some way you're getting 0.999... that I do not know of?  

Are we talking about two different 0.999...'s because I don't think it would be a fixed object.

If we talk about 1/9 * 9 or 1/3 * 3 (or whatever else way people use to get 0.999 and 1 being the same thing), to some extent I agree that those two numbers are representing the same thing.  I do not agree, however, that 0.999... as an infinity is 1. 

It's fixed in the same way that Pi or E are fixed.


Not really.  



Faxanadu on 30 April 2013

Of course it is. That is basic math at university level.



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