Poll: 0.999... = 1

[Lukeje]

Simple reason to ignore the "proofs" for 0.9999 to equal 1 is this:

The definition of "infinity".

When i to any halfway sane person say "0. and then add an infinite amount of 9's" then by golly, all that will follow WILL be 9's. Infinite times 9 means infinite times 9. Any PHD that claims otherwise can go fuck themselves and die in a corner, for abusing authority to claim that a tautology is false.

How they are "proving" that 0.999... is equal to 1, is be REDEFINING infinity and the rules to handle it. In other words, they keep the words, but change the meaning. That is called cheating.

No. Your intuitive understanding of infinity is not the general mathematical understanding of infinity. It is you that are redefining infinity to fit your intuitive understanding.

 

[Rabid Toilet]

Snip

I'm not saying that there arent other good ideas backing it up to be "true." I'm just saying that this is the same logic that explains how the holocaust started. Someone of authority said something was right, and the people followed.

and dont tell me it has nothing to do with this, because it has everything to do with the reasoning behind as to why some believe its right and others dont.

And yet someone in authority said that 2 + 2 = 4, and the people followed.

Why does 2 + 2 = 4? Because they say so.

Using the very laws of mathematics that were invented so long ago by those people, .99... and 1 are the same number.

because 2+2=4 is based on the idea of two.... somethings... apples. Two apples, plus two apples. equals four apples. Its volume, its real, its there.

And yet we have imaginary numbers, we have pi. These aren't real, they aren't there, and yet we accept that they exist, that we can use them, and that they are true.

FYI pi is a real number pi is the ratio of the circumference to the radius of the same circle
imaginary numbers are negative square root and do not cross the x intercept i think

Dammit, alright fine, I'll do one more post, but then I'm going to bed!

Pi is an irrational number, in that it can't be expressed as a fraction. Thus, you can't have pi apples, it's not physically possible. Just like you can't have an infinite number of nines after the decimal place.

Imaginary numbers do not exist, because they do not appear on the number line. Thus, you can't have the square root of -1 apples. Just like you can't have an infinite number of nines after the decimal place.

And yet we accept that these things are real, and we use them as though they are true. That's the comparison I was making.

Now seriously, stop quoting me, I'm leaving.

 

[Lukeje]

Snip

I'm not saying that there arent other good ideas backing it up to be "true." I'm just saying that this is the same logic that explains how the holocaust started. Someone of authority said something was right, and the people followed.

and dont tell me it has nothing to do with this, because it has everything to do with the reasoning behind as to why some believe its right and others dont.

And yet someone in authority said that 2 + 2 = 4, and the people followed.

Why does 2 + 2 = 4? Because they say so.

Using the very laws of mathematics that were invented so long ago by those people, .99... and 1 are the same number.

because 2+2=4 is based on the idea of two.... somethings... apples. Two apples, plus two apples. equals four apples. Its volume, its real, its there.

And yet we have imaginary numbers, we have pi. These aren't real, they aren't there, and yet we accept that they exist, that we can use them, and that they are true.

FYI pi is a real number pi is the ratio of the circumference to the radius of the same circle
imaginary numbers are negative square root and do not cross the x intercept i think

I think they meant them to be separate elements in a list; they weren't implying that pi is imaginary.

 

[Lyx]

No. Your intuitive understanding of infinity is not the general mathematical understanding of infinity. It is you that are redefining infinity to fit your intuitive understanding.

In that case, i rather trust my "intuitive definition", which is based on actual observation what happens and logical considerations about what our minds CAN mean by saying "infinity", rather than some invented claims without proof (unless one considers an axiom a proof - i don't, and never will).

 

[Lukeje]

No. Your intuitive understanding of infinity is not the general mathematical understanding of infinity. It is you that are redefining infinity to fit your intuitive understanding.

In that case, i rather trust my "intuitive definition", which is based on actual observation what happens and logical considerations about what our minds CAN mean by saying "infinity", rather than some invented claims without proof (unless one considers an axiom a proof - i don't, and never will).

You've observed infinity?

 

[Lyx]

No. Your intuitive understanding of infinity is not the general mathematical understanding of infinity. It is you that are redefining infinity to fit your intuitive understanding.

In that case, i rather trust my "intuitive definition", which is based on actual observation what happens and logical considerations about what our minds CAN mean by saying "infinity", rather than some invented claims without proof (unless one considers an axiom a proof - i don't, and never will).

You've observed infinity?

I have observed what happens when the concept of infinity is applied And that is plain repetition. The "program" doesn't even contain the "instruction" to make the leap which you'd like it to make. Which is why infinity cannot exist - it doesn't ever make any final statement... it just repeats without ever "returning".

 

[Jaime_Wolf]

Simple reason to ignore the "proofs" for 0.9999 to equal 1 is this:

The definition of "infinity".

When i to any halfway sane person say "0. and then add an infinite amount of 9's" then by golly, all that will follow WILL be 9's. Infinite times 9 means infinite times 9. Any PHD that claims otherwise can go fuck themselves and die in a corner, for abusing authority to claim that a tautology is false.

How they are "proving" that 0.999... is equal to 1, is be REDEFINING infinity and the rules to handle it. In other words, they keep the words, but change the meaning. That is called cheating.

With this, i do not mean to say that there is no reason for changing the meanings. There may well be - but if you change the meaning, then please also change the words, because else you're quite simply deceiving people.

If for example we hypothetically were to define "@n" to mean "as close as possible to n", then 0.9 associated with the operator @1 would indeed mean "well, here we have 0.9, make that as close as possible to 1", and obviously, the ideal return value would indeed be 1. Which is quite different to saying "infinite times 9". There are other ways to achieve it. I dont care which one they use, its all fine by me, as long as what the symbols mean equals how they are used.

Or we could go the metaphysics route, by questioning if a value can even be infinitely precise, and if there always for practical reasons will be some inaccuracy. That too is okay by me.

But FFS, do not say "infinite times 9", and then do something else.

But we're talking about the same infinity. We're ALL talking about .999 followed by an infinite number of nines. Some of the proofs require that you correctly extrapolate from that same concept of infinity, but that's not the same as saying that there are different concepts of infinity at work. We have the same basic concept of infinity, many people are just wrong about the ramifications of that concept. It's like asking someone to multiply humongous numbers in their head: there's a very good chance they'll get the wrong answer, but that's not because they're using a different multiplication, they're just making an error in a very difficult computation. Extrapolating from a basic idea of infinity is a very, very difficult computation.

The biggest problem though is that you're trying to characterise .999... as a process: give me the closest number that's less than one, but isn't one.

.999... is a number, not a process. It is, in fact, a number that is equal in value to 1. If you still don't want to believe that a number can have two representations, you should take a look at the link I posted earlier showing independent reasoning about why a number system often assigns two representations to the same real number.

Here's the link: http://en.wikipedia.org/wiki/.999...#Impossibility_of_unique_representation

There are also some problems with your conception of tautology. I cannot for the life of me think of the name of the problem, but the canonical example has to do with the sentence "The Morningstar is the Eveningstar." The example is from Wittgenstein if I remember correctly. If anyone can think of the name, that might be helpful.

Edit: People saying that your intuitive idea of infinity is wrong are...wrong. Your intuitive idea of infinity is the only idea of infinity that exists. The theory of mathematics you have built is, however, flawed in the ways it EXTRAPOLATES from the basic concept you share with virtually everyone. You can pretty handily show that the theory you form from those extrapolations it isn't internally consistent and that the theory used in mathematics is essentially the only logical extension of your basic intuition.

 

[BiscuitTrouser]

Actually, it didn't :-/ That proof works.

Third last step, at 2a(a-b) = a(a-b). a = b, so dividing by (a-b) is impossible. Yet they still do. So no.

The third last step is still valid, because a-b = 0, so both sides equal 0.

You could just as easily say

532531521215a(a-b) = a(a-b)
532531521215 = 1

which is equally as wrong.

If x = 0.999999...
Then 10x = 9.9999...
Therefore, 10x - x = 9
Which implies 9x = 9
Thus, x = 1
x also = 0.99999...

In conclusion, I have just proven 1 = 0.9999...

You're doing it wrong, too. At step 4, 9x = 9, that is not true.

9x = 8.99999999



Edit: I'm not even a math major, but the amount of ignorant false intellectualism in this thread is about to make me cry.

Dont mock these people, this proof is correct. Let me write it differently for you.

EDIT: I see what you did there... your saying x = 1 because 0.999 rec = 1. So 9x SHOULD be 8.999

1/3 = 0.333 recurring. times 0.33 recurring by three. You know have 0.9999 recurring logically. However you have 3/3 if written as a fraction. This shows that 3/3 = 0.999 recuring AND 3/3 also = 1. Therefor 0.999 reccuring must also = 1.

No infinites there, just fractions of an irational nature. These are logical. These work. You cannot tell me that 3/3 does not = 1 but that 1/3 = 0.33333 recuring. These are both true. Leading to the logical conclusion that 0.99999 recurring = 1.

10x = 9.9999 .... to one less infinite place value

Im sorry did you just say infinite minus 1... Do you have any idea how the infinite works?! Its a concept not a number. You cannot have one less infinite value... that doesnt make any sense. Infinite cannot be edited by any normal functions of math, it is INFINITE nothing you do can make it larger or smaller because it is already of infinite size. Anything smaller than the infinite ISNT the infinite. I think you know what youre talking about but you worded it wrong. Sorry if thats the case, it just reminded me of idiot class mates asking about infinity and going:

"Is infinity plus 1 larger than infinity?"

This irks me.

 

[Lyx]

@Jaime

I disagree. .999... is a process, not a number. I have never seen anything else, and i cannot even MEAN anything else... this is not just a matter of "imagination".... the value which you claim infinity is, is not constructable in our minds. It also isn't constructable in a machine. In fact, it NOWHERE is constructable.

It does not exist. All that exists is a looped process.

 

[smithy_2045]

@Jaime

I disagree. .999... is a process, not a number. I have never seen anything else, and i cannot even MEAN anything else... this is not just a matter of "imagination".... the value which you claim infinity is, is not constructable in our minds. It also isn't constructable in a machine. In fact, it NOWHERE is constructable.

It does not exist. All that exists is a looped process.

Infinity is a concept, not a number, not a process.

 

[Jaime_Wolf]

Actually, it didn't :-/ That proof works.

Third last step, at 2a(a-b) = a(a-b). a = b, so dividing by (a-b) is impossible. Yet they still do. So no.

The third last step is still valid, because a-b = 0, so both sides equal 0.

You could just as easily say

532531521215a(a-b) = a(a-b)
532531521215 = 1

which is equally as wrong.

If x = 0.999999...
Then 10x = 9.9999...
Therefore, 10x - x = 9
Which implies 9x = 9
Thus, x = 1
x also = 0.99999...

In conclusion, I have just proven 1 = 0.9999...

You're doing it wrong, too. At step 4, 9x = 9, that is not true.

9x = 8.99999999



Edit: I'm not even a math major, but the amount of ignorant false intellectualism in this thread is about to make me cry.

Dont mock these people, this proof is correct. Let me write it differently for you.

EDIT: I see what you did there... your saying x = 1 because 0.999 rec = 1. So 9x SHOULD be 8.999

1/3 = 0.333 recurring. times 0.33 recurring by three. You know have 0.9999 recurring logically. However you have 3/3 if written as a fraction. This shows that 3/3 = 0.999 recuring AND 3/3 also = 1. Therefor 0.999 reccuring must also = 1.

No infinites there, just fractions of an irational nature. These are logical. These work. You cannot tell me that 3/3 does not = 1 but that 1/3 = 0.33333 recuring. These are both true. Leading to the logical conclusion that 0.99999 recurring = 1.

As has been repeatedly stated, that proof is extremely problematic in that most only accept that 1/3 = .333... because they've been conditioned to do so. The equations don't actually explain how or why .000...=1 in any serious way.

You need analytic proofs or proofs from the construction of the real numbers to really shed light on the question. I think every such well-known proof has already been posted and people should really be looking at those rather than trying to cling to these algebraic proofs.

 

[Subzerowings]

If x equals 0.999...
Then doesn't 10x equal 9.999....9990?

 

[Lyx]

Infinity is a concept, not a number, not a process.

Last time i checked, concepts can be processed (though, i guess that depends on how one defines "concept")

 

[Lukeje]

No. Your intuitive understanding of infinity is not the general mathematical understanding of infinity. It is you that are redefining infinity to fit your intuitive understanding.

In that case, i rather trust my "intuitive definition", which is based on actual observation what happens and logical considerations about what our minds CAN mean by saying "infinity", rather than some invented claims without proof (unless one considers an axiom a proof - i don't, and never will).

You've observed infinity?

I have observed what happens when the concept of infinity is applied And that is plain repetition. The "program" doesn't even contain the "instruction" to make the leap which you'd like it to make. Which is why infinity cannot exist - it doesn't ever make any final statement... it just repeats without ever "returning".

If the program stops in finite time, then it has not reached infinity. Thus you cannot have observed infinity.

 

[Lyx]

No. Your intuitive understanding of infinity is not the general mathematical understanding of infinity. It is you that are redefining infinity to fit your intuitive understanding.

In that case, i rather trust my "intuitive definition", which is based on actual observation what happens and logical considerations about what our minds CAN mean by saying "infinity", rather than some invented claims without proof (unless one considers an axiom a proof - i don't, and never will).

You've observed infinity?

I have observed what happens when the concept of infinity is applied And that is plain repetition. The "program" doesn't even contain the "instruction" to make the leap which you'd like it to make. Which is why infinity cannot exist - it doesn't ever make any final statement... it just repeats without ever "returning".

If the program stops in finite time, then it has not reached infinity. Thus you cannot have observed infinity.

Exactly my point

 

[Knusper]

I read this in the newspaper a few years back, and the evidence they had for it then was:

1/3 = 0.3333333...
therefore: 3/3 (which equals 1) = 0.99999...

and so therefore you have proof that 0.999... = 3/3 = 1

Also, can you think of a number which is bigger than 0.999... but smaller than 1? No? Well then they must be the same.

 

[Lukeje]

No. Your intuitive understanding of infinity is not the general mathematical understanding of infinity. It is you that are redefining infinity to fit your intuitive understanding.

In that case, i rather trust my "intuitive definition", which is based on actual observation what happens and logical considerations about what our minds CAN mean by saying "infinity", rather than some invented claims without proof (unless one considers an axiom a proof - i don't, and never will).

You've observed infinity?

I have observed what happens when the concept of infinity is applied And that is plain repetition. The "program" doesn't even contain the "instruction" to make the leap which you'd like it to make. Which is why infinity cannot exist - it doesn't ever make any final statement... it just repeats without ever "returning".

If the program stops in finite time, then it has not reached infinity. Thus you cannot have observed infinity.

Exactly my point

So what are you arguing? Just that the differentiation between 0.(9) and 1 makes no difference in the real world, and is as such just an intellectual exercise? I don't think anyone would deny that.

 

[Woodsey]

Yes.

We had this thread come up so many times at once a few months ago that anyone left not understanding why it is should be shot spoken to.

 

[Lyx]

Exactly my point

So what are you arguing? Just that the differentiation between 0.(9) and 1 makes no difference in the real world, and is as such just an intellectual exercise? I don't think anyone would deny that.

I'm argueing that the only thing someone has ever seen of infinity, is the process towards "infinity" - for a reason

(the unquoted infinity and quoted "infinity" have different meanings)


P.S.: That for practical applications (i.e. computations in programs to do something in the real world), there is no difference between 1 and 0.999... stopped at sufficient accuracy, i'd never deny. The discussion is irrelevant for practical applications in tech.... it does however have strong conceptual rammifications.... things like mathematical points for example are used a lot in physics - and as a result, physics claims that there are objects in reality that contain infinities.

 

[quhouv vhqwiufv qwiu]

Actually, it didn't :-/ That proof works.

Third last step, at 2a(a-b) = a(a-b). a = b, so dividing by (a-b) is impossible. Yet they still do. So no.

The third last step is still valid, because a-b = 0, so both sides equal 0.

You could just as easily say

532531521215a(a-b) = a(a-b)
532531521215 = 1

which is equally as wrong.

If x = 0.999999...
Then 10x = 9.9999...
Therefore, 10x - x = 9
Which implies 9x = 9
Thus, x = 1
x also = 0.99999...

In conclusion, I have just proven 1 = 0.9999...

You're doing it wrong, too. At step 4, 9x = 9, that is not true.

9x = 8.99999999



Edit: I'm not even a math major, but the amount of ignorant false intellectualism in this thread is about to make me cry.

Dont mock these people, this proof is correct. Let me write it differently for you.

EDIT: I see what you did there... your saying x = 1 because 0.999 rec = 1. So 9x SHOULD be 8.999

1/3 = 0.333 recurring. times 0.33 recurring by three. You know have 0.9999 recurring logically. However you have 3/3 if written as a fraction. This shows that 3/3 = 0.999 recuring AND 3/3 also = 1. Therefor 0.999 reccuring must also = 1.

No infinites there, just fractions of an irational nature. These are logical. These work. You cannot tell me that 3/3 does not = 1 but that 1/3 = 0.33333 recuring. These are both true. Leading to the logical conclusion that 0.99999 recurring = 1.

As has been repeatedly stated, that proof is extremely problematic in that most only accept that 1/3 = .333... because they've been conditioned to do so. The equations don't actually explain how or why .000...=1 in any serious way.

You need analytic proofs or proofs from the construction of the real numbers to really shed light on the question. I think every such well-known proof has already been posted and people should really be looking at those rather than trying to cling to these algebraic proofs.

You can use long division to prove that 1/3 = 0.333...