Matter /CAN/ be created!

[Vigormortis]

Clegane]

SNIP

I don't know why you bothered posting that long wall of text. People have known that matter can be created for over 60 years and theres no need for all that garbage, it can be summed up in one line. Ready?

E=MC^2

There, that's all it takes. E is energy, M is matter. It's been extensively proven (for 1000s of years) that we can make energy from matter and therefore it must be possible to recreate matter from energy. Which Einstein conclusively proved in the 40s or 50s or whatever.

I think you're wording is a bit off.

The 'creation' of matter is impossible. Queue long winded explanation of the law of thermodynamics. However, energy can be 'converted' into matter. And vice-versa. That's the difference.

Also, it hasn't been thousands of years. It's barely been over a century since we've understood this fact.

 

[Lukeje]

there is no way to represent infinity, or an infinite recurrence, on a number line, except for an approximation.

That's why you use extensions of the number line.

http://en.wikipedia.org/wiki/Riemann_sphere

 

[ACman]

^ That's where you made your error, if you multiply X and the value of X in this equation by 10, that means there's 1 less '9' than in just X, infinity - 1 '9's, if that helps; so 10X-X (9X) would equal 0.000...1 in the infinity place, basically.

You're dealing with infinitesimals here, and of course by definition infinitesimals can't be measured, and so will lead to errors if you try to use them in equations.

In short, .999... does NOT = 1, OP is wrong.

Ummmmmmmmmmmmm.

1/3 = 0.3 rep

2/3 = 0.6 rep

3/3 = ?

 

[The_root_of_all_evil]

there is no way to represent infinity, or an infinite recurrence, on a number line, except for an approximation.

That's why you use extensions of the number line.

http://en.wikipedia.org/wiki/Riemann_sphere

But that confounds the problem because the only way of creating a recurring decimal is the decimal approximation of a fraction. (Pi or e don't count as they don't recur precisely - that's why they have a name)

Therefore, everytime you see a .1rep or .4rep, you KNOW that it's actually talking about a fraction; because there's no other way to create one. We don't have the technology to measure anything that could have one.

So, .9rep is already 1 (which is what people think), because .9rep is a decimal approximation of a fraction.

Start with x = 0.999rep

means x=1.

Multiply .1rep by 9 and you get 1. That's how it works. Riemann sphere's aren't necessary as we already know where the recurrence came from - approximations.

The bit where the whole argument breaks down is that x=0.9rep, right at the start. It's a mathematic bait/switch just like sawing the lady in half. Or tenths.

 

[geizr]

f(x) = 1 - 10-x
f(0) = 0
f(1) = 0.9
f(2) = 0.99
f(3) = 0.999
limx→∞ f(x) = 1

And the hidden zero thing is rubbish.

Your function only approaches 1 in the limit, but it never actually gets there. This is because n/(infinity) only approaches zero in the limit; it never actually gets there. However, for purposes of convenience, we often ignore that subtlety because it is below our error tolerance, but, when we need to be more mathematically precise, we can not make that assertion.

It's not a trick. 0.999... = 1.

Yes, it is a trick because it is ignoring the underlying cardinality.

Infinity doesn't really have a size, as such.

Infinity very much has a size, and that size can be different in different cases. That is why you can take the limit of a numerator and denominator both going to infinity and, yet, obtain a finite ratio. It's because they are different sized infinities.

There is no "at the end". Recurring decimals are endless.

It doesn't matter how endless they are, you can always add one more digit to make a larger infinity. That's what happens when you multiply by 10.

So 1 ≠ 1.0 because they have a different number of digits? ("hidden zero")

Numerically, yes, that is precisely true. The number 1 does not have the same precision as 1.0. The representation 1.0 is, at best, an approximation of the number 1. As I said above, for most practical purpose, it is below our error tolerance, so we don't care. But, when we need to be more mathematically precise, we do care.

As a result, 10*x - x =/= 9.0000rep; there is a hidden 1 all the way at the last digit.

There is no "last digit".

EDIT: I should have pointed out that cardinality is the size of a set, and it can be used to deal with infinite sets like 0.999rep.

0.999... is not a set. It's a number.

The digits that we use to represent numbers are sets. Each element in the set represents a particular fraction multiplied by some factor. The arithmetic operations with which we are familiar perform transformations on those elements, which can themselves be sets. When you multiply x = 0.999rep by 10, you shift all the elements upward and then have to add an extra empty set element at the very end to represent the digit that was vacated as a result of the multiplication. Now, when you do the subtraction, the very last element in 0.999rep, is matched against an empty set element rather than another 9, hence why you don't get 9, exactly, but something infinitesimally smaller than 9.

This is necessarily nonsense. It's something that happens precisely because infinity is not the same size everywhere. It doesn't always have the same meaning. Just like I can not label all the real numbers with integers because there is a greater infinity of real numbers than there is the infinity of integers. They are not the same size infinities. That's the cardinality difference.

EDIT: Correction. You don't get something infinitesimally larger than 9; you get something infinitesimally smaller than 9.

 

[OrokuSaki]

If you thought that was cool, here's some Astrophysics 101.

There is a gravitational attration between EVERY object. The equation to calculate that attration is:

Fg=G((M1 * M2)/D^2)

Where
Fg= The force of gravity
G= Universal gravity constant (don't worry about it, it's a really small number)
M1 and M2= Mass of object 1 and 2
D= distance

Now that we have that established...
Black holes have such huge masses that not even light can escape it.
You're probably putting two and two together now...
If you look at the equation, for that statement to be true both objects must have a mass.
Light has mass.

According to a documentary on black holes that I watched, physicists hate'em because once you get to a certain point near the singularity, that (or some other physics gravity equation) comes out to a big-fat infinity sign staring up at you, suggesting that a singularity has infinite mass and infinite gravity.

I'm definitely not a physicist, but I do know the meaning of the words "Infinite" and "Gravity". Wouldn't an object with infinite gravity consume EVERYTHING regardless of distance? Because if it's truly infinite then it doesn't decrease, 1/2 of infinity is still infinity because infinity goes on forever and cannot be decreased. So if a black hole has infinite gravity wouldn't we all be dead?

 

[Makhiel]

It doesn't matter how endless they are, you can always add one more digit to make a larger infinity. That's what happens when you multiply by 10.

That's not what happens, one more item added to a set that has the cardinality of infinity will result in a set the cardinality of which is still infinity (infinity of the same "size"). You need to do more than adding items to reach higher cardinality.

 

[randomsix]

If you thought that was cool, here's some Astrophysics 101.

There is a gravitational attration between EVERY object. The equation to calculate that attration is:

Fg=G((M1 * M2)/D^2)

Where
Fg= The force of gravity
G= Universal gravity constant (don't worry about it, it's a really small number)
M1 and M2= Mass of object 1 and 2
D= distance

Now that we have that established...
Black holes have such huge masses that not even light can escape it.
You're probably putting two and two together now...
If you look at the equation, for that statement to be true both objects must have a mass.
Light has mass.

According to a documentary on black holes that I watched, physicists hate'em because once you get to a certain point near the singularity, that (or some other physics gravity equation) comes out to a big-fat infinity sign staring up at you, suggesting that a singularity has infinite mass and infinite gravity.

I'm definitely not a physicist, but I do know the meaning of the words "Infinite" and "Gravity". Wouldn't an object with infinite gravity consume EVERYTHING regardless of distance? Because if it's truly infinite then it doesn't decrease, 1/2 of infinity is still infinity because infinity goes on forever and cannot be decreased. So if a black hole has infinite gravity wouldn't we all be dead?

The force gravity of a BH is only infinite arbitrarily close to the singularity.

Because the D in the above equation is zero, and you're dividing by it.

Make D a more reasonable number, and the force is finite.

And photons do not have mass. The reason that light cannot escape black holes is that the gravity of the BH bends space to the extent that local space around the BH is falling into the hole at a speed faster than c.

 

[Lukeje]

there is no way to represent infinity, or an infinite recurrence, on a number line, except for an approximation.

That's why you use extensions of the number line.

http://en.wikipedia.org/wiki/Riemann_sphere

But that confounds the problem because the only way of creating a recurring decimal is the decimal approximation of a fraction. (Pi or e don't count as they don't recur precisely - that's why they have a name)

Therefore, everytime you see a .1rep or .4rep, you KNOW that it's actually talking about a fraction; because there's no other way to create one. We don't have the technology to measure anything that could have one.

So, .9rep is already 1 (which is what people think), because .9rep is a decimal approximation of a fraction.

Start with x = 0.999rep

means x=1.

Multiply .1rep by 9 and you get 1. That's how it works. Riemann sphere's aren't necessary as we already know where the recurrence came from - approximations.

The bit where the whole argument breaks down is that x=0.9rep, right at the start. It's a mathematic bait/switch just like sawing the lady in half. Or tenths.

We're talking about completely separate issues here. Representing infinity as a number requires an extension of the `number line' (by which, to be clear, I mean the set of real numbers). So does representation of the number generated by the square root of -1.

A completely separate issue is that of the representation of repeating decimals as fractions. This does not require any extension of the real numbers. Every repeating decimal can be mapped into at least one fractional representation. This may be proved to varying degrees of rigour if one has the time or inclination. And you're right; 0.(9) is equivalent to 1 by definition. (The definition is that 0.(0)1 is equivalent to zero, if you were wondering).

I also don't understand why you think that the only non-repeating decimals are those that have names. One can easily prove that there is a set of size aleph[sub]1[/sub] that don't.

(I've also noticed that you seem confused by the notion of mathematical equivalence. Saying that a is equivalent to b means that a=b if and only if b=a. Equivalence thus implies equality).

 

[dobahci]

This is hilarious. It's funny how there's another thread where the vast majority of Escapist readers believe themselves to be of above average intelligence, and then you have this thread, where a sizable quantity of readers prove themselves unable to comprehend what is essentially grade school mathematics.

 

[RJ 17]

If you thought that was cool, here's some Astrophysics 101.

There is a gravitational attration between EVERY object. The equation to calculate that attration is:

Fg=G((M1 * M2)/D^2)

Where
Fg= The force of gravity
G= Universal gravity constant (don't worry about it, it's a really small number)
M1 and M2= Mass of object 1 and 2
D= distance

Now that we have that established...
Black holes have such huge masses that not even light can escape it.
You're probably putting two and two together now...
If you look at the equation, for that statement to be true both objects must have a mass.
Light has mass.

According to a documentary on black holes that I watched, physicists hate'em because once you get to a certain point near the singularity, that (or some other physics gravity equation) comes out to a big-fat infinity sign staring up at you, suggesting that a singularity has infinite mass and infinite gravity.

I'm definitely not a physicist, but I do know the meaning of the words "Infinite" and "Gravity". Wouldn't an object with infinite gravity consume EVERYTHING regardless of distance? Because if it's truly infinite then it doesn't decrease, 1/2 of infinity is still infinity because infinity goes on forever and cannot be decreased. So if a black hole has infinite gravity wouldn't we all be dead?

Which is precisely why physicists HATE singularities. There shouldn't BE a big fat double-helix looking back at you when considering gravity and mass...and yet all the calculations for all the physics we as humans understand all break down once you get within a certain distance of a singularity.

 

[someonehairy-ish]

How has this got anything to do with matter being created? I thought you might be on about nuclear fusion, not a maths trick designed to confuse 15 year olds...

No. A 15 year old shouldn't be tricked at all. For one, it's not a trick at all, and two, I learned this in math class when I was like 11 and I understood it then.

What would you call it, if not a trick? What word denotes exactly what that piece of maths is? I don't know. It's not relevant anyway. And that age was plucked out of the air too.

My point was that a) nobody is impressed by this and b) the content has nothing to do with the title.

 

[The_root_of_all_evil]

I also don't understand why you think that the only non-repeating decimals are those that have names. One can easily prove that there is a set of size aleph[sub]1[/sub] that don't.

It's one of those falsehoods you tell so that people don't get confused when you start going into Set Theory, Game Theory and d2x/dy2. Aleph sets are cardinality of infinite sets, so they don't naturally occur.

(I've also noticed that you seem confused by the notion of mathematical equivalence. Saying that a is equivalent to b means that a=b if and only if b=a. Equivalence thus implies equality).

From what I can tell, the terminology has changed somewhat. My Maths training was back in the early 90s; pre-Windows 3.1. We had the three bar equals as equivalent, but it seems the approximation (curved upper bar) has taken over. (BODMAS to us was Brackets Over, not Brackets Operand)

But .9rep is only equivalent to 1, where as 1 can be .9rep - the infinite repetition is a flag that it approximates for convenience - so it can be used but not without loss of accuracy.

 

[Lukeje]

I also don't understand why you think that the only non-repeating decimals are those that have names. One can easily prove that there is a set of size aleph[sub]1[/sub] that don't.

It's one of those falsehoods you tell so that people don't get confused when you start going into Set Theory, Game Theory and d2x/dy2. Aleph sets are cardinality of infinite sets, so they don't naturally occur.

I think your terminology is very confused. The cardinality (i.e. number of elements in the set) is aleph[sub]1[/sub]. And please stop using buzzwords that have nothing to do with the topic at hand (i.e. game theory and the reference to calculus); they do nothing but muddy your posts in irrelevance.

(I've also noticed that you seem confused by the notion of mathematical equivalence. Saying that a is equivalent to b means that a=b if and only if b=a. Equivalence thus implies equality).

From what I can tell, the terminology has changed somewhat. My Maths training was back in the early 90s; pre-Windows 3.1. We had the three bar equals as equivalent, but it seems the approximation (curved upper bar) has taken over. (BODMAS to us was Brackets Over, not Brackets Operand)

Again, that has nothing to do with the topic at hand.

But .9rep is only equivalent to 1, where as 1 can be .9rep - the infinite repetition is a flag that it approximates for convenience - so it can be used but not without loss of accuracy.

This is gibberish.

 

[The_root_of_all_evil]

This is gibberish.

Then stop reading. I've tried to explain, but your rudeness - once again - seems to overide your critical thinking.

 

[burningdragoon]

How has this got anything to do with matter being created? I thought you might be on about nuclear fusion, not a maths trick designed to confuse 15 year olds...

No. A 15 year old shouldn't be tricked at all. For one, it's not a trick at all, and two, I learned this in math class when I was like 11 and I understood it then.

What would you call it, if not a trick? What word denotes exactly what that piece of maths is? I don't know. It's not relevant anyway. And that age was plucked out of the air too.

My point was that a) nobody is impressed by this and b) the content has nothing to do with the title.

Well I guess I was more speaking towards the "designed" part of what you said not so much the "trick" part. Or rather, 0.9 repeating being equal to 1 is not a trick on it's own, but it is being presented as such. Like 'tricking' people by saying a tomato is a fruit even though it is used more like a vegetable. Or something I dunno.

Your actual point I agree with. This whole thread is silly. (a bad kind of silly at that)

 

[OrokuSaki]

The force gravity of a BH is only infinite arbitrarily close to the singularity.

Because the D in the above equation is zero, and you're dividing by it.

Make D a more reasonable number, and the force is finite.

And photons do not have mass. The reason that light cannot escape black holes is that the gravity of the BH bends space to the extent that local space around the BH is falling into the hole at a speed faster than c.

So I think I have a limited understanding here, you're saying that the gravity of the black hole is only infinite in the center, and that it somehow becomes weaker the farther away from it you are?

I didn't think that infinity could work that way, but live and learn I guess.

 

[someonehairy-ish]

How has this got anything to do with matter being created? I thought you might be on about nuclear fusion, not a maths trick designed to confuse 15 year olds...

No. A 15 year old shouldn't be tricked at all. For one, it's not a trick at all, and two, I learned this in math class when I was like 11 and I understood it then.

What would you call it, if not a trick? What word denotes exactly what that piece of maths is? I don't know. It's not relevant anyway. And that age was plucked out of the air too.

My point was that a) nobody is impressed by this and b) the content has nothing to do with the title.

Well I guess I was more speaking towards the "designed" part of what you said not so much the "trick" part. Or rather, 0.9 repeating being equal to 1 is not a trick on it's own, but it is being presented as such. Like 'tricking' people by saying a tomato is a fruit even though it is used more like a vegetable. Or something I dunno.

Your actual point I agree with. This whole thread is silly. (a bad kind of silly at that)

Ahhh ok I see what you mean. I meant 'trick' more in the sense of... a bike trick or something? A trick in the sense of a minor feat, rather than trick in the sense of intentionally mislead.
Not only silly, but flamebait too!

 

[Lukeje]

This is gibberish.

Then stop reading. I've tried to explain, but your rudeness - once again - seems to overide your critical thinking.

Likewise. Once you bother to investigate some of the topics you keep name dropping, then maybe we can have a proper discussion.

 

[RJ 17]

Wow, I never really expected I'd get this huge of a response based off of a simple mathematical trick.

For all of those lured into this topic with the promise of some grand revelation about physics and the nature of the universe, I do apologize, and have already been warned by mods about having a misleading topic title (though technically the title was actually a joke playing off the fact that, were my math correct as it has been proven to be wrong, the 0.---1 that makes 0.999rep = 1 seems to come out of nowhere...thus "matter" (more specifically a number) is created).

Personally I'd like to consider this topic as a "sense of humor check". And while a varying degree of a lack of sense of humor has been displayed by various people taking my OP and the title of this topic too seriously, it seems as though one person has gone so far as to threaten me with an admin report. So we'll see if I get to hang around or if I might be taking a leave of absence here in a bit...though this being my first offense, maybe they'll just stick me on probation if the charges stick.

Anyways, I do sincerely hope you've at least enjoyed the interesting mathematical conversations/debates that have sprung up as a result of my numbers trick. As your resident Random Jester, all I ever seek is to entertain. :3