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New .999.. = 1 thread

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Isn't this just an argument between mathematic proof (it is) and human, logical proof (it isn't)? We've seen a million different mathematical proofs that all say the same thing - enough that I think it's safe to conclude that maths in general says that it's equal.

Then again there's the nice human argument that 'if it were equal to 1, it would be written as 1. If it's not it's not equal.'

Can't maths be used to prove that movement is impossible? You can prove anything with maths 😱
 
Originally posted by: Allio
Isn't this just an argument between mathematic proof (it is) and human, logical proof (it isn't)? We've seen a million different mathematical proofs that all say the same thing - enough that I think it's safe to conclude that maths in general says that it's equal.

Then again there's the nice human argument that 'if it were equal to 1, it would be written as 1. If it's not it's not equal.'

Can't maths be used to prove that movement is impossible? You can prove anything with maths 😱
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The human argument that you propose is flawed. For there is multiple ways to write things that are equal. 1, 1.0, 2/2, 100%, 100e-2.

What is the proof that movement is impossible? I believe I can find a false claim in it.
 
Originally posted by: TuxDave
The human argument that you propose is flawed. For there is multiple ways to write things that are equal. 1, 1.0, 2/2, 100%, 100e-2.

What is the proof that movement is impossible? I believe I can find a false claim in it.
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Good point. I don't think I really summarised what I meant quite how I meant to... I guess it's to do with the way we as humans have a difficult time comprehending infinity.

I can't find you the proof, I'm sorry... I vaguely remember hearing it being demonstrated a few years ago. I'm probably completely wrong.

As I've never studied calculus I don't quite feel qualified to participate in this thread 😉
 
I miss the other thread. Thanks for starting this one.

Always enjoy watching finite beings assuming knowledge of the infinite 🙂


 
ok i am starting to agree with you guys that .99999=1, but how do you go about explaining this to people who are EXTREMELY set on it being wrong??
 
You should have re-started the poll to give some of the 500+ people who said no a chance to change their vote!
 
Originally posted by: DrPizza
Originally posted by: SagaLore
Originally posted by: zbalat
1/3 = .3333333333.....................

1/3 + 1/3 + 1/3 = 1

so 1= .9999999999999999999999999999999999999....................................................

It's so simple. I can't believe it is such an issue on this forum.
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.333..., .666..., .999... do not exist. Repeating numbers are an imaginary construct to get by with the flaw of the decimal system. Only whole integers and ratios can represent accurate values when dealing with partials.

I would conclude that even .3333... does not equal 1/3.
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I'm not sure I'd call it a "flaw." Furthermore, the concept that "only whole integers and ratios can represent accurate values when dealing with partials" died around the time of Pythagoras. If you disagree, then give me the precise value of the diagonal of a square with sides of length 1. I'll be content with sqrt(2). But, that cannot be represented as a ratio. (and the proof is fairly simple if you need it)
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Right, I don't disagree - but to represent a number with sqrt(2) is a ratio representation. Otherwise I'd be using 1.41421356. 2 is a whole integer and much more accurately dealt with.

 
"What is the smallest positive number?"

Specifically: if we define the variable d as the answer to this question, then the real number system fails to provide a well-defined numeric value for d.

We can cause the real number system to fail in other ways by asking other questions, such as: "What is 1 divided by 0?", or "What is the square root of -1?". (The real number system is perhaps not as robust as you might have assumed.)

Each time another failure occurs in the real number system, it triggers the creation of another branch of mathematics. The failure to find a real value for d triggers the creation of the hyperreal number system, which is an extension to the real number system that allows us to give a well-defined value to d by creating the concept of infinitesimal numbers that are distinct from 0.
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Why does there need to be a smallest possible postive number? Also how would you represent d in the hyperreal number systeM?
 
The argument boils down to whether you're using the standardly constructed Reals, and accept the base assumptions of that construction as absolute (questionable, but understandable). Every proof I've seen so far in this "rehash" thread implicitly assumes a standard construction of the Reals.

Some mathematicians reconstruct the Reals in such a way that 0.99...!=1 by definition, allowing them to tackle string theory problems and other advanced physics problems that are intractable using the standard Reals. You can reconstruct everything useful in Calculus with either approach (most texts use the standard Reals). If you want the links to those mathematicians' work, dig through the old thread and find them yourselves.

The most important argument, of course, is the final poll tally on the locked thread:
42.279999...% yes it is.
48.86% no it isn't.
8.86% huh?
😛
 
Originally posted by: MrDudeMan
ok i am starting to agree with you guys that .99999=1, but how do you go about explaining this to people who are EXTREMELY set on it being wrong??
Click to expand...

You ask them what's the difference between 0.999... and 1. In other words what is 1-0.999...?

The answer is 0, because you can never finish putting more 9s down for 0.999...

so there is no 0.000000000...1 because that 1 never comes up. The zeroes go on forever, hence 1-0.999...=0, so mathematically they are both the same.

You see you don't need advanced math for this. All it requires is an understanding of the word infinite.
 
I give this one a

0,99999999999999999999999999999999999999999999999999999999999999999999999999999999999/10

just for the effort.
 
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