Is 1 = 0.9999......

[ElFenix]

Originally posted by: MadRat

Originally posted by: ElFenix
hey, heres an idea, subtract .999... from 1. tell me what you get. an infinite number of 0s. what is 0? its nothing. what do you have when you have an infinite amount of nothing? you still have nothing! its still 0! it doesn't matter how many decimal places you carry the answer out its still 0!

That would be a proof to say ".999... does not exist" but does not prove .999...=1.

no if you subtracted something that didn't exist from 1 you'd still have 1.

 

[silverpig]

Originally posted by: MadRat
Which points confuse you?

The idea that .999... doesn't fit on the number line? That just begs the question of what is the number closest to 0 which is not zero? I've claimed that if it exists then a difference between 1 and itself exists; if it does not exist then the argument is moot. The human mind cannot comprehend infinity therefore no man can define infinity in any objective terms. You can believe that the idea of infinity exists but it cannot be proven because it is a purely subjective value.

Saying that .999... is to 1 what 4/2 is to 2 is yet another absurdity. It has no relevance to the argument.

There is no number closest to 0. It is fairly easy to see why.

It does not exist, so how is the 0.999... = 1 argument moot? You have just supposed that there is no number closest to any other, so therefore 0.999... cannot be the closest number to 1 without being 1. So there either must be a number closer to 1, or it must equal 1. This is one of the main ideas here. You cannot find a number between 0.999... and 1 because they are equal.

There are no objective values. They are all subjective in their construction.

 

[silverpig]

I would still appreciate explanations to the following points:

"At the same time if you accept that .999... does exist then there must be a difference between 1 and that number."

Please find me this difference.

"You've only shown how to make .333... into 1/3 with hocus pocus of using a limit as the definition of the product to gain an even numbered product, which cannot happen."

Again, are you saying that 1 is even now?

"Saying that .999... is to 1 what 4/2 is to 2 is yet another absurdity. It has no relevance to the argument."

Please explain why this is absurd.

 

[MadRat]

Originally posted by: ElFenix

Originally posted by: MadRat

Originally posted by: ElFenix
hey, heres an idea, subtract .999... from 1. tell me what you get. an infinite number of 0s. what is 0? its nothing. what do you have when you have an infinite amount of nothing? you still have nothing! its still 0! it doesn't matter how many decimal places you carry the answer out its still 0!

That would be a proof to say ".999... does not exist" but does not prove .999...=1.

no if you subtracted something that didn't exist from 1 you'd still have 1.

Exactly why either .999... does not exist or if it does exist then there must be a number equally close to zero w/o being zero.

Silverpig-

Are you trying to say that all math is moot because none of it is objective? I certainly hope not. The principles of math lie within a set of objectives. The answers become subjective when the equation does not have a single solution. The idea that .999=1 is more paradigm than solution. What is necessary to make it true turns around and makes it false.

 

[SilentRunning]

O.K. Madrat I guess I will have to see if silverpig can read and comprehend.

For silverpig's edumacation

Please understand the difference between giving a value to and equaling.

 

[ElFenix]

Originally posted by: MadRat

Originally posted by: ElFenix

Originally posted by: MadRat

Originally posted by: ElFenix
hey, heres an idea, subtract .999... from 1. tell me what you get. an infinite number of 0s. what is 0? its nothing. what do you have when you have an infinite amount of nothing? you still have nothing! its still 0! it doesn't matter how many decimal places you carry the answer out its still 0!

That would be a proof to say ".999... does not exist" but does not prove .999...=1.

no if you subtracted something that didn't exist from 1 you'd still have 1.

Exactly why either .999... does not exist or if it does exist then there must be a number equally close to zero w/o being zero.

Silverpig-

Are you trying to say that all math is moot because none of it is objective? I certainly hope not. The principles of math lie within a set of objectives. The answers become subjective when the equation does not have a single solution. The idea that .999=1 is more paradigm than solution. What is necessary to make it true turns around and makes it false.

ok.... if theres a number out there between .999... and 1 tell me what it is. or between 0.000... and 0. either one.

 

[MadRat]

Originally posted by: silverpig
I would still appreciate explanations to the following points:
"At the same time if you accept that .999... does exist then there must be a difference between 1 and that number."
Please find me this difference.
"You've only shown how to make .333... into 1/3 with hocus pocus of using a limit as the definition of the product to gain an even numbered product, which cannot happen."
Again, are you saying that 1 is even now?
"Saying that .999... is to 1 what 4/2 is to 2 is yet another absurdity. It has no relevance to the argument."

Please explain why this is absurd.

What two equal negative numbers equal a negative number as a product? The impossible logic used to solve this is the same impossible logic to solve for infinity, leaving infinity safely outside human comprehension. We have to use abstract and illogical definitions to represent them.

 

[NovaTone]

Originally posted by: MadRat

Originally posted by: silverpig
I would still appreciate explanations to the following points:
"At the same time if you accept that .999... does exist then there must be a difference between 1 and that number."
Please find me this difference.
"You've only shown how to make .333... into 1/3 with hocus pocus of using a limit as the definition of the product to gain an even numbered product, which cannot happen."
Again, are you saying that 1 is even now?
"Saying that .999... is to 1 what 4/2 is to 2 is yet another absurdity. It has no relevance to the argument."

Please explain why this is absurd.

What two equal negative numbers equal a negative number as a product? The impossible logic used to solve this is the same impossible logic to solve for infinity, leaving infinity safely outside human comprehension. We have to use abstract and illogical definitions to represent them.

i


i * i = -1

 

[Darien]

Originally posted by: NovaTone

Originally posted by: MadRat

Originally posted by: silverpig
I would still appreciate explanations to the following points:
"At the same time if you accept that .999... does exist then there must be a difference between 1 and that number."
Please find me this difference.
"You've only shown how to make .333... into 1/3 with hocus pocus of using a limit as the definition of the product to gain an even numbered product, which cannot happen."
Again, are you saying that 1 is even now?
"Saying that .999... is to 1 what 4/2 is to 2 is yet another absurdity. It has no relevance to the argument."

Please explain why this is absurd.

What two equal negative numbers equal a negative number as a product? The impossible logic used to solve this is the same impossible logic to solve for infinity, leaving infinity safely outside human comprehension. We have to use abstract and illogical definitions to represent them.

i


i * i = -1

And i is used in the Schrodinger equation

link

 

[SilentRunning]

Originally posted by: Darien

Originally posted by: NovaTone

Originally posted by: MadRat

Originally posted by: silverpig
I would still appreciate explanations to the following points:
"At the same time if you accept that .999... does exist then there must be a difference between 1 and that number."
Please find me this difference.
"You've only shown how to make .333... into 1/3 with hocus pocus of using a limit as the definition of the product to gain an even numbered product, which cannot happen."
Again, are you saying that 1 is even now?
"Saying that .999... is to 1 what 4/2 is to 2 is yet another absurdity. It has no relevance to the argument."

Please explain why this is absurd.

What two equal negative numbers equal a negative number as a product? The impossible logic used to solve this is the same impossible logic to solve for infinity, leaving infinity safely outside human comprehension. We have to use abstract and illogical definitions to represent them.

i


i * i = -1

And i is used in the Schrodinger equation

link

And i is imaginary

And by that I mean the symbol i is imaginary not that I personally am imaginary. 😀

 

[Darien]

Originally posted by: SilentRunning

Originally posted by: Darien

Originally posted by: NovaTone

Originally posted by: MadRat

Originally posted by: silverpig
I would still appreciate explanations to the following points:
"At the same time if you accept that .999... does exist then there must be a difference between 1 and that number."
Please find me this difference.
"You've only shown how to make .333... into 1/3 with hocus pocus of using a limit as the definition of the product to gain an even numbered product, which cannot happen."
Again, are you saying that 1 is even now?
"Saying that .999... is to 1 what 4/2 is to 2 is yet another absurdity. It has no relevance to the argument."

Please explain why this is absurd.

What two equal negative numbers equal a negative number as a product? The impossible logic used to solve this is the same impossible logic to solve for infinity, leaving infinity safely outside human comprehension. We have to use abstract and illogical definitions to represent them.

i


i * i = -1

And i is used in the Schrodinger equation

link

And i is imaginary

What's in a name? 😉

 

[silverpig]

Originally posted by: MadRat

Originally posted by: silverpig
I would still appreciate explanations to the following points:
"At the same time if you accept that .999... does exist then there must be a difference between 1 and that number."
Please find me this difference.
"You've only shown how to make .333... into 1/3 with hocus pocus of using a limit as the definition of the product to gain an even numbered product, which cannot happen."
Again, are you saying that 1 is even now?
"Saying that .999... is to 1 what 4/2 is to 2 is yet another absurdity. It has no relevance to the argument."

Please explain why this is absurd.

What two equal negative numbers equal a negative number as a product? The impossible logic used to solve this is the same impossible logic to solve for infinity, leaving infinity safely outside human comprehension. We have to use abstract and illogical definitions to represent them.

That answered nothing.

And i*i = -1

i is imaginary, but that's just a name for the set of numbers dealing with i. They could be called "other" numbers, or "orange" numbers... whatever.

 

[SilentRunning]

Originally posted by: silverpig


That answered nothing.

Did you even read the link I provided?

Do you still not comprehend the difference between giving an approximate value to a non-terminating decimal and finding an equality for it.

 

[Skyclad1uhm1]

1/infinity = 0
Infinitely small does not exist, it just equals 0. Else 0.999... would not equal 1.

 

[Mookow]

Originally posted by: BruinEd03

Originally posted by: Kyteland

Originally posted by: spidey07
Contains the series and actual proof

http://mathforum.org/dr.math/faq/faq.0.9999.html

I actually showed that same proof to two of my coworkers earlier and they said that the limits thing is still an approximation because the summation never terminates.

I think they are full of it.

Congratulations, your co-workers have just destroyed the foundation for caclulus 🙂

-Ed

Does this mean I wont have to take any more calculus classes?

 

[schizoid]

Maybe this has been said before, but it is my understanding that the "proof" or whatever just shows that multiplication doesn't work on infinite series, not that .999 = 1. Or maybe that's the proof that 1 = 2. I can never remember which. But the point is that sure, the proof works, it's just that our number system doesn't allow for some of the operations provided.

Or something.

It's tired.

And I have to finish my damn personal statement for this damn fellowship.

And I hate everything.

Especially you.

 

[Kyteland]

Originally posted by: SilentRunning

Q: How many mathematicians does it take to convince computer programmer types that 0.999... was indeed the same as 1 at Kyteland's workplace?

A: Three, but two of them must have PHD's and ignore that fact that wasn't the question that was asked.

HAHA! That's funny.

It seems to me that the original question was "What do you think?" I never asked anyone to prove anything to me. I simply wanted a simple poll to see what the general consensus was among a group of people similarly composed to that of my work environment and I did exactly that.

And in spite of any argument for or against "is 1=0.9999....." presented here, we managed to convince a largely skeptical group if intelligent people that we were probably right.

 

[yoda291]

whoa, Highly Technical deja vu!

I still can't find the old thread in HT tho...

 

[silverpig]

Originally posted by: SilentRunning

Originally posted by: silverpig


That answered nothing.

Did you even read the link I provided?

Do you still not comprehend the difference between giving an approximate value to a non-terminating decimal and finding an equality for it.

Do you realize I was posting in reply to MadRat?

I read the link, I know the difference between giving a value and finding what it equals.

The value given to 0.999... is the limit of the sum, this limit equals 1.

 

[JupiterJones]

Originally posted by: Czar
1.000000000000000000000000000000000000000000000000000000000000000...... = 1
0.999999999999999999999999999999999999999999999999999999999999999...... ~= 1

just depends how you round it
its like saying that 1/3 is the same as 0.3, which it isnt

The point to the actual solution is that you don't round it.

In brief,

By definition, For any A>C, there must exist B such that A-B>C. Let A=1, Let C=0.9999999999999999... No matter what B is selected (0.1, 0.000000001, 0.0000...0001, etc.) this does not work. Therefore A=C.

 

[Martin]

As an engineering student, I say yes. 🙂

 

[SilentRunning]

Originally posted by: silverpig

I read the link, I know the difference between giving a value and finding what it equals.

The value given to 0.999... is the limit of the sum, this limit equals 1.

So you get, I thought you were one of the ones who thought 1 = 0.99999...

They are not equal but the are given the same value. That is the concept that people here do not seem to grasp. That is why my tag line is what it is. Yes 1 and 0.9999... are the same value for mathematical purposes due to the approximation for 0.9999..., but they are not truely equal.

They thread asked only one question are the two numbers equal, not do we treat them as the same value.

 

[bleeb]

hmm i never thought this post would generate such a HUGE response.

 

[petrek]

They are not equal but they are given the same value. That is the concept that people here do not seem to grasp. That is why my tag line is what it is. Yes 1 and 0.9999... are the same value for mathematical purposes due to the approximation for 0.9999..., but they are not truely equal.

The thread asked only one question are the two numbers equal, not do we treat them as the same value.

Exactly.

D

(Edit: fixed grammatical errors in the quote)

 

[SpecialEd]

i hate decimals... they cause soo many problems...