Matter /CAN/ be created!

[Makhiel]

the underscore is my way of saying "repeating", the number after the underscore is my way of saying "at the end of this infinitely repeating number is an 8, or a 7."

Yes I am aware of how odd it is to try an place a number at the end of an infinite.

I didn't ask what the underscore meant.
And yes, it's so odd that it is impossible. As such none of your proofs in which you've used it is valid.

 

[oktalist]

Yes I am aware of how odd it is to try an place a number at the end of an infinite.

It's not just odd, it's completely backwards and meaningless.

You are wasting your time trying to disprove this "proof". The "proof" presupposes the proposition that it is trying to prove, a proposition that happens to be true, so the only way to disprove it is with a "disproof" that presupposes the contradictory proposition.

 

[irishda]

Except that we are trying to prove x=x, that's the point of the exercise.
0.999... = 1 is a widely accepted mathematical fact. This is not a bunch of people on a forum going 'Look I'm a genius and I proved this new thing', it's a guy going 'Hey I learnt this and thought it was super cool it (which it is) but I overestimated its significance'

Personally I'm a much bigger fan of the simpler approach (which has been shown here before).

1/3 = 0.333...
1/3 * 3 = 0.333... * 3
3/3 = 0.999...
1 = 0.999...

It's really just as simple as that.

Now, I'm not going to go and call anyone an idiot for disbelieving this, it doesn't seem right, in a way it's nice to see so many people try to apply critical thinking to the problem, and not just assuming its correct (though let's face it, that's really coming about because they heard it from a guy on the internet).

That's the point isn't it? They are one and the same number.

The OP's original equations don't show .999r=1 because the math is off. It's like that riddle about the waiter splitting a $30 bill three ways and losing $3. The logic is just slightly off.

9(.999r) =/= 9

The assumption is made in the original equation that 9x=9, but 9(.999r) is only 8.99r. 9(.999r) will equal 9 only if you already go into the equation with the assumption that .999r=1. If we ACTUALLY go through the equation by replacing the x with .999r (since that's what x is supposed to equal) we get the TRUE result of the equation.

.999r=.999r
10(.999r)=10(.999r)
9.99r=9.99r
9.99r-.999r=9.99r-.999r
9=9
9/9=9/9
1=1

OR substitute the opposite

x=x
10x=10x
10x-x=10x-x
9x=9x
x=x

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.

 

[Makhiel]

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

But 8.99r is 9.

 

[Truth Cake]

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)

And obviously 3 divided by 3 is 1, plain and simple.

 

[Wyes]

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).

 

[Wyes]

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)

And obviously 3 divided by 3 is 1, plain and simple.

I must I must double post; 0.333... and their ilk are not approximations. If you try to take them to some amount of decimal places, then yes, they are approximations, but they go on to infinity! There is no 'error'.

 

[irishda]

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

 

[Truth Cake]

I must I must double post; 0.333... and their ilk are not approximations. If you try to take them to some amount of decimal places, then yes, they are approximations, but they go on to infinity! There is no 'error'.

You could've just edited your first pose to include the quote and response...

And yes, they ARE approximations, all non-terminating decimals are approximations since a precise amount in decimal form would have infinite numbers, which obviously cannot be written out or measured.

Put it this way: if you just have 3/3 by itself, as in 3 divided by 3, as in how many groups of 3 marbles can you make out of a whole set of 3 marbles? 1 group. Not .999... group(s), 1 group.

 

[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.

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.

 

[Maze1125]

But that confounds the problem because the only way of creating a recurring decimal is the decimal approximation of a fraction.

This seems to be the root of your confusion, your assumption that infinite decimals are just approximations.

They are not. An infinite decimal is defined as the limit of a series, and limits are precise. Specifically, if we're defining decimal 0.x[sub]1[/sub]x[sub]2[/sub]x[sub]3[/sub]x[sub]4[/sub]..., then the series that defines it is sum[sub]n=1[/sub][sup]m[/sup](x[sub]n[/sub]/10[sup]n[/sup]) and the limit of that series is, of course, sum[sub]n=1[/sub][sup]infinity[/sup](x[sub]n[/sub]/10[sup]n[/sup]).

Now, with the decimal 0.999..., x[sub]n[/sub]=9 for all n.
Therefore the sequence that defines the decimal is sum[sub]n=1[/sub][sup]m[/sup](9/10[sup]n[/sup]), and the limit of that is sum[sub]n=1[/sub][sup]infinity[/sup](9/10[sup]n[/sup]), which can be proven to be precisely 1 (I hope you don't need me to do that bit, but I can if you wish me to).

Further, the exact same method can be used to prove that recurring decimal notation of fractions are not approximations either, but are also precise.

 

[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.