Matter /CAN/ be created!

[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

 

[Lukeje]

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)

It's easy to write something that repeats to an infinite number of decimal places. There have been examples throughout the thread. Unless you mean writing out `long-hand' in which case the fact that you can't is kind of the point. What's neat is that because of its repeating nature we can actually see how it behaves as the number of decimal places tends to infinity.

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?"

Ermm... 8.(9) is a rational number; it can be written 9/1 (or 18/2, etc.).

 

[Maze1125]

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

That's just a red herring, as I said before, you just grasping at statements made in the proof, rather than at the reasoning between those statements.
Yes, the proof says that 9x = 9 where x = 0.999..., but that claim is not just pulled out the air, it is deduced from the previous statements. You can't just attack the statement while ignoring the reasoning the produced it.

Anyway, here's a subtly different way of arriving and the same claim:

0.999... * 10 - 0.999... = 0.999... * 9

Agreed? I mean, that's pretty basic, if you take a number and multiply by 10, then take one lot of that number away, you've got the number multiplied by 9 instead.

0.999... * 10 - 0.999... = 9.999... - 0.999... = 9

0.999... * 9 = 8.999...

I should hope these are both clearly true too.

So, one side of the original equation equals 9, and the other equals 8.999..., also, we know from the first part that the two sides are also equal to each other.
Therefore 9 and 8.999... must also be equal.