Matter /CAN/ be created!

[irishda]

Either way you don't get .999r=1

As for the fractions, I understand you need to know fractals in order to refute that one, but it's still refutable.

As with most mathematical proofs (particularly in mathematical induction), you presuppose that what you're trying to prove is true. Then, if it is true, it's all internally consistent; if it's not true, there is some contradiction which breaks the internal consistency.

In the proof using fractions, we are working under the assumption 1/3 = 0.333...
This is the key step. Most people do not question this step, because it is elementary. If you disagree with it, then we'll never agree.
If you are interested in other proofs, there's a geometric series proof here [http://www.purplemath.com/modules/howcan1.htm], though you'll only accept this one if you can accept that what we know about geometric series is correct.

As for refutability; these are not 'refutable' because they are facts, it doesn't matter how much you know about infinitives, transinfinitives or fractals, they remain true. Maybe some day we will discover we were wrong, but it hasn't happened yet, and I doubt that anybody here is going to be the person to disprove it (but hey, stranger things have happened).

Except they're proofs with logical fallacies, like saying "All cats are red. I have a cat. Therefore I have a red cat." I've already refuted the algebraic proof, and, while I don't have the necessary knowledge to refute the fraction, I did explain it to someone else who was knowledgeable enough to be able to laugh at it.

 

[Maze1125]

The assumption is made in the original equation that 9x=9, but 9(.999r) is only 8.99r.

But 8.99r is 9.

Again, only if you already believe that .999r=1. But that's changing the math to suit your belief. It doesn't change the fact that 9x=8.999r. If you divide that by 9, then oh look at that, you get x=.99r. Not x=1

You're misreading the original proof.
That 9x = 9, was not assumed, it was deduced from the previous statements.

Let x = 0.999...

=>

10x = 9.999...

=>

10x - x = 9.999... - x

as chosen, x = 0.999...
=>

10x - x = 9.999... - 0.999...

Therefore

9x = 9

and x = 1

 

[Truth Cake]

Once again, this is dealing with infinitesimals, which cannot be measured

It's got nothing to do with measurement, and there is no infinitesimal involved.

Traditionally one poses some sort of evidence when arguing a point, not just saying 'you're wrong!'...

I'll be blunt- 1/3 does not QUITE equal .333... (and by proxy, 2/3 doesn't quite equal .666...), that's just as close as we can come to measuring it since we can't write something to the infinity decimal place. (unless you've found a way that I don't know about, which no offense, but I highly doubt)

We have found a way to write infinity decimal places. That's what the ... on the end of .333... means.

My reply to that is 'yes and no'. Since just the same we can't write it out in the infinity place using real numbers, it's just more of what's in between the decimal point and the supposed infinity place that it supposedly represents.

It really doesn't matter, obviously neither of us is going to convince the other they're wrong, so we may as well stop before we waste more of each other's time- let's just agree to disagree, and get on with our lives.

 

[ACman]

Ummmmmmmmmmmmm.

1/3 = 0.3 rep

2/3 = 0.6 rep

3/3 = ?

Once again, this is dealing with infinitesimals, which cannot be measured, so there's bound to be stupid little errors like that when you try to measure them (or leave out measuring them when they're supposed to be included, as the case may be).

I'll be blunt- 1/3 does not QUITE equal .333... (and by proxy, 2/3 doesn't quite equal .666...), that's just as close as we can come to measuring it since we can't write something to the infinity decimal place. (unless you've found a way that I don't know about, which no offense, but I highly doubt)

http://stickerish.com/wp-content/uploads/2011/04/JackiechanBlackSS.png

Yes it does!!!!!!!!!!

1/3 = 0.3 repeating

And there are several algebreic and anaytical proofs that 0.9 repeating equals 1.

Either algebra is incorrect or you are.

There is no real number that equals 1 - 0.9repeating that is not zero.

 

[Maze1125]

Once again, this is dealing with infinitesimals, which cannot be measured

It's got nothing to do with measurement, and there is no infinitesimal involved.

Traditionally one poses some sort of evidence when arguing a point, not just saying 'you're wrong!'...

You're shifting the burden of proof.

You're the one claiming that infinitesimals play a role in this, and because of that we can't do the calculations. So you have to prove that claim.

To claim that you have to do three things:
a) Define what an infinitesimal is in the context of the mathematics we're using.
b) Show where infinitesimals by your definition exist in the problem
and
c) Show how those infinitesimals cause problems.

Otherwise you're basically just saying "You can't do that, you haven't taken into account the Quazgarsens!"

I'll be blunt- 1/3 does not QUITE equal .333... (and by proxy, 2/3 doesn't quite equal .666...), that's just as close as we can come to measuring it since we can't write something to the infinity decimal place. (unless you've found a way that I don't know about, which no offense, but I highly doubt)

We have found a way to write infinity decimal places. That's what the ... on the end of .333... means.

My reply to that is 'yes and no'. Since just the same we can't write it out in the infinity place using real numbers, it's just more of what's in between the decimal point and the supposed infinity place that it supposedly represents.

We know that, lots and lots of 9s.
Just because we can't write it out, doesn't mean we can't know what's there or how to mathematically manipulate it. For a precise definition, see my post a few above yours.

 

[Truth Cake]

Yes it does!!!!!!!!!!

1/3 = 0.3 repeating

And there are several algebreic and anaytical proofs that 0.9 repeating equals 1.

Either algebra is incorrect or you are.

I never said algebra is wrong, just the proofs that claim that .999... = 1, which it doesn't.

And once again, 1/3 DOES NOT = .333..., that's just as close as we can come to measuring it- since you're repeating the same thing you've already said, I'll do the same.

As I've already said to someone else, there's no point in us arguing since obviously neither of us is going to convince the other they're wrong, so let's just agree to disagree and move on, this is getting no one anywhere.

 

[Truth Cake]

For a precise definition, see my post a few above yours.

I guess you completely missed the last part of my last post- I don't care anymore. You're not going to convince me if you write 30 volumes on the theory of infinity or whatever, and I figure I'm not any more likely to convince you likewise; I'm done arguing and I'm moving on with my life, I suggest you do the same.

Edit- double post, sorry, I thought I was quoted after my last post... my bad.

 

[Wyes]

Except they're proofs with logical fallacies, like saying "All cats are red. I have a cat. Therefore I have a red cat." I've already refuted the algebraic proof, and, while I don't have the necessary knowledge to refute the fraction, I did explain it to someone else who was knowledgeable enough to be able to laugh at it.

Actually, if you make the assumption all cats are red, there's no logical problems with that argument. Now, if you'd said something like "All cats are red. I have a red pet. Therefore I have a cat," then yes, there is a logical fallacy there. But this is just me being pedantic and has no bearing on the topic really.

I'm not trying to be rude but you have refuted nothing, because you made errors in your attempt at a disproof (as you must have, because this is a fact. I cannot stress this enough, this is a widely accepted mathematical fact. I study maths, this is what I do).

If we define x = 0.999... (which we can do, because we are awesome and have the power to set the value of variables, we are not in this instance presupposing 0.999... = 1, it simply falls out of the maths), then the following process makes complete sense.

x = 0.999...
10*x = 10 * 0.999...
10x = 9.999... (if you disagree with this step, one of us is doing algebra very, very wrong)
10x - x = 9.999... - x (at this stage, remember that we DEFINED x = 0.999...)
9x = 9 (this seems to be what you're disagreeing with, but it seems elementary to me that 9.999... - 0.999... = 9. If you'd like, you can look at it a different way; (9 + 0.9 + 0.09 + 0.009 + ...) - (0.9 + 0.09 + 0.009 + ...) = 9. You can see clearly that 0.9 subtracts from 0.9 to leave 0, and 0.09 subtracts from 0.09 to leave 0 and so on, until all we are left with is 9).
And obviously from here,
x = 1, meaning 0.999... = 1.

It really doesn't matter, obviously neither of us is going to convince the other they're wrong, so we may as well stop before we waste more of each other's time- let's just agree to disagree, and get on with our lives.

B-but... somebody is wrong on the internet! =P
This does seem wise.

 

[Maze1125]

Yes it does!!!!!!!!!!

1/3 = 0.3 repeating

And there are several algebreic and anaytical proofs that 0.9 repeating equals 1.

Either algebra is incorrect or you are.

I never said algebra is wrong, just the proofs that claim that .999... = 1, which it doesn't.

And once again, 1/3 DOES NOT = .333..., that's just as close as we can come to measuring it- since you're repeating the same thing you've already said, I'll do the same.

As I've already said to someone else, there's no point in us arguing since obviously neither of us is going to convince the other they're wrong, so let's just agree to disagree and move on, this is getting no one anywhere.

For a precise definition, see my post a few above yours.

I guess you completely missed the last part of my last post- I don't care anymore. You're not going to convince me if you write 30 volumes on the theory if infinity or whatever, and I figure I'm not any more likely to convince you likewise; I'm done arguing and I'm moving on with my life, I suggest you do the same.

What I get from those two posts is that you're going to refuse to read anything more on the subject, but still insist you're right. That doesn't make any sense.

If you care about this subject, sure keep insisting you're right, but also keep reading up on it.

If you don't care enough to read those bits, why do you need to insist you're right? Surely it doesn't really matter to you and you can just accept it's a subject you don't really know much about and it quite likely that, somewhere in all the stuff you're not going read, someone has proven you're wrong.

Care, or don't care, I don't mind, but claiming you don't care while still insisting you're right makes no sense.

 

[ACman]

Yes it does!!!!!!!!!!

1/3 = 0.3 repeating

And there are several algebreic and anaytical proofs that 0.9 repeating equals 1.

Either algebra is incorrect or you are.

I never said algebra is wrong, just the proofs that claim that .999... = 1, which it doesn't.

And once again, 1/3 DOES NOT = .333..., that's just as close as we can come to measuring it- since you're repeating the same thing you've already said, I'll do the same.

As I've already said to someone else, there's no point in us arguing since obviously neither of us is going to convince the other they're wrong, so let's just agree to disagree and move on, this is getting no one anywhere.

There is no real number that equals 1 - 0.9repeating that is not zero.

 

[ACman]

]

For a precise definition, see my post a few above yours.

I guess you completely missed the last part of my last post- I don't care anymore. You're not going to convince me if you write 30 volumes on the theory of infinity or whatever, and I figure I'm not any more likely to convince you likewise; I'm done arguing and I'm moving on with my life, I suggest you do the same.

Edit- double post, sorry, I thought I was quoted after my last post... my bad.

This isn't a matter of opinion. You are wrong and apparently joyously revelling in your ignorance.

There is no real number that is infinitly small and thus 0.9repeating = 1

 

[oktalist]

Once again, this is dealing with infinitesimals, which cannot be measured

It's got nothing to do with measurement, and there is no infinitesimal involved.

Traditionally one poses some sort of evidence when arguing a point, not just saying 'you're wrong!'...

0.999... = Luke Skywalker

Prove me wrong. With evidence.

 

[Atmos Duality]

Irrational/repeating numbers are just a precise measurement of a quantity; they are NOT asymptotes. Hell, they aren't even functions.
Ultimately, they are just numbers. Nothing more.

But even if I create a function: y = 1/3 (0.333_ rep), the line doesn't move any closer to any real axis you can define for any given x value; it stays precisely at 1/3.
If it were an asymptote, it would move closer at some point.

If I create the function y = 3/3, it is a form of 1, and thus has two representations (actually, infinite); a rational integer, and a repeating number. No matter which one you choose, they are the same precise quantity.
Remember: there are an infinite number of ways to represent the quantity '1'.

 

[ACman]

I'll be blunt- 1/3 does not QUITE equal .333... (and by proxy, 2/3 doesn't quite equal .666...), that's just as close as we can come to measuring it since we can't write something to the infinity decimal place. (unless you've found a way that I don't know about, which no offense, but I highly doubt)

Using long division, a simple division of integers like 1⁄3 becomes a recurring decimal, 0.333?

Is long division wrong or are you?

 

[Robert Ewing]

Doesn't really prove that matter can be created (or destroyed.)

It's just a mathematical trick that would make some guys in MIT chuckle a bit. And I know that maths can be applied to everything, but in this case, it's hard to relate it.

 

[irishda]

Except they're proofs with logical fallacies, like saying "All cats are red. I have a cat. Therefore I have a red cat." I've already refuted the algebraic proof, and, while I don't have the necessary knowledge to refute the fraction, I did explain it to someone else who was knowledgeable enough to be able to laugh at it.

Actually, if you make the assumption all cats are red, there's no logical problems with that argument. Now, if you'd said something like "All cats are red. I have a red pet. Therefore I have a cat," then yes, there is a logical fallacy there. But this is just me being pedantic and has no bearing on the topic really.

I'm not trying to be rude but you have refuted nothing, because you made errors in your attempt at a disproof (as you must have, because this is a fact. I cannot stress this enough, this is a widely accepted mathematical fact. I study maths, this is what I do).

If we define x = 0.999... (which we can do, because we are awesome and have the power to set the value of variables, we are not in this instance presupposing 0.999... = 1, it simply falls out of the maths), then the following process makes complete sense.

x = 0.999...
10*x = 10 * 0.999...
10x = 9.999... (if you disagree with this step, one of us is doing algebra very, very wrong)
10x - x = 9.999... - x (at this stage, remember that we DEFINED x = 0.999...)
9x = 9 (this seems to be what you're disagreeing with, but it seems elementary to me that 9.999... - 0.999... = 9. If you'd like, you can look at it a different way; (9 + 0.9 + 0.09 + 0.009 + ...) - (0.9 + 0.09 + 0.009 + ...) = 9. You can see clearly that 0.9 subtracts from 0.9 to leave 0, and 0.09 subtracts from 0.09 to leave 0 and so on, until all we are left with is 9).
And obviously from here,
x = 1, meaning 0.999... = 1.

Actually multiply 9 by .999r though and see what you come up with.

 

[ACman]

Actually multiply 9 by .999r though and see what you come up with.

It's 8.9 repeating.

Or 9.

Because they are the same thing.

 

[Wyes]

Actually multiply 9 by .999r though and see what you come up with.

As ACman said, it's 8.999..., which is equal to 9.


EDIT: Actually I'm going to quote some comments off facebook from one of my former lectures on this topic;
"On a psychological level the presence of infinity is secondary -- the first hurdle is multiple representations for real numbers.
This particular confusion somehow doesn't come up with rational numbers -- since when did you hear anybody argue that 1/2 and 3/6 weren't the same number?"

 

[spartan231490]

This is the most bs proof I've ever seen, and I've seen it before. You eliminate the portion of the decimal that repeats, proving nothing. This proof really proves that decimals can't accurately relate some fractions, and that's really all that it proves.

 

[ACman]

This is the most bs proof I've ever seen, and I've seen it before. You eliminate the portion of the decimal that repeats, proving nothing. This proof really proves that decimals can't accurately relate some fractions, and that's really all that it proves.

Excuse me?

Doesn't 0.333333333333333 repeating forever equal 1/3?

A decimal representation of a non-negative real number r is an expression of the form of a series, traditionally written as a sum:

http://upload.wikimedia.org/wikipedia/en/math/5/a/f/5afe758496f193d1e7628c3aeb8cadc7.png

For 0.999... one can apply the convergence theorem concerning geometric series:

http://upload.wikimedia.org/wikipedia/en/math/5/9/4/5944b421545ee7150a09a891231a1855.png

Since 0.999... is such a sum with a common ratio r = 1⁄10, the theorem makes short work of the question:

http://upload.wikimedia.org/wikipedia/en/math/5/6/9/56949181a290ce561f27bd550a720392.png