Matter /CAN/ be created!

[isometry]

The Banach-Tarski paradox comes much closer to "creating matter from nothing", but of course it doesn't apply either since matter consists of discrete particles, not an uncountable continuum.

Anyway, the Banach-Tarski paradox is a surprising theorem that says it's possible to break a sphere into a finite number of non-overlapping pieces, and combine the pieces to make two whole spheres which are each the same size as the original.

The catch is that the non-overlapping pieces are all unmeasurable sets. Each is a subset of the sphere and the pieces don't overlap, but beyond that it's impossible to visualize the pieces - they would look like dense fractals.

Here is the wikipedia article on this interesting theorem:

http://en.wikipedia.org/wiki/Banach?Tarski_paradox

OT: Yeah 1 = 0.9999..., two different ways of writing the same number. Also 2.2 = 2.199... , etc.

 

[triggrhappy94]

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.

Yeah. If you look at the equation, the pull gets exponentially greater after you get bellow one meter apart.

 

[GoAwayVifs]

Oh great, this thread. Again. There is no infinitesimal difference. There is no rounding. There is no error in math. 0.999... is exactly equal to 1.

 

[RavenGlenn]

That doesn't mean matter can be created though. It just means that .999 repeating is the same as 1.

But how can 0.999_ = 1 when 0.999_ is meant to represent a number infinitely close to 1 without actually being 1? Where does the extra 0.(insert infinite line of zeros)1 come from that bumps all the 9s ahead of it to 10s, thus making it 1?

The easiest way to prove that 0.999... is equal to 1 is this: What can you add to 0.999... to make it equal 1?

The answer to that question is "Nothing". Therefore, 0.999... is equal to 1.

It's a pretty basic principle of math.

 

[Tiger Sora]

Dear math, please stop trying to arouse the professors of your department. It's cutting productivity which equates to us losing money. You don't want us to have to cut your budget do you.

 

[Berenzen]

Any mathematician will tell you that .999... is equal to 1. This is because 0.000...1 does not exist. A mathematician could explain it better than I can.

The closest way that we can create matter is by converting energy into it. However, Mass and Energy must be conserved unless you want to get into insane multidimensional physics that is no more than conjecture.

The equation to Mass-Energy equivalence is E^2=γm^2c^4 + γp^2c^2. Where γ= (1/sqrt(1-(v^2/c^2))

Light has mass-energy equivalence depending on the energy of the photon. Measured in MeV (Mega electronVolts), energy is affected by gravity because of warping in space-time, as defined through general relativity.

A black hole has a definite mass, and in fact it can be calculated by the size of it's schwartzchild radius- radius of the event horizon. Equation is r=2GM/c^2. All matter has a schwartzchild radius, but most of them are contained within the actual particles itself.

F=GMM/r^2 cannot equal infinite. Even as you approach the center of a black hole it does not equal infinite. However, it approaches it asymptotically. In order for an object to have infinite gravitational attraction to another object, it must exist at the exact same location of the other object, a physical impossibility.

People, before you start spewing out physics, you should probably take a physics/astronomy course beforehand, instead of just looking at equations and thinking you know it.

 

[SL33TBL1ND]

That doesn't mean matter can be created though. It just means that .999 repeating is the same as 1.

But how can 0.999_ = 1 when 0.999_ is meant to represent a number infinitely close to 1 without actually being 1? Where does the extra 0.(insert infinite line of zeros)1 come from that bumps all the 9s ahead of it to 10s, thus making it 1?

It doesn't come from anywhere, you proved that 0.9... = 1 in your post with the algebra. Why are you refuting your own work? Not only that, but this doesn't have anything to do with matter being created. What on Earth are you on about?

http://en.wikipedia.org/wiki/0.999...

 

[chuckey]

I'm sorry but .999... is not, nor ever will be equal to 1. Just think of it this is 1 = 2? no? well the same concept applies to this. 1 is not equal to .999... no matter how many 9s there are there will always just be a little bit missing.

Another way is to think about asymptotes in graphs.

Spoiler: asymptote

(this is just and image of a regular asymptote, not related to the scenario I'm explaining.)

Let's say that your asymptote boundaries are X=1 and y=1. That means that no matter how close to the boundary the line will get i.e. .999... it will never touch it because that will mean that 1 would be a solution to the equation of the graph, which for equations with asymptotes would not be possible because it would cause a 0 to appear in the denominator of the original equation. (equations that have asymptote have a variable in the denominator i.e. Y= 1/(X-1).)

Therefore .999... cannot equal 1.

EDIT: forget just saw the wiki article, egh I guess I'm just stubborn. DAMN you CALCULUS TEACHER!!!

 

[Rabid Toilet]

Oh god, this thread again. It's such an easy way to get a hundred pages of back and forth between those who understand complicated math and those who don't. I refuse to get sucked into another debate about this. It simply never ends.

Yes, .999... is exactly equal to 1. No, it does not involve rounding. They are exactly the same number. No, I'm not going to spend time explaining all of the different proofs and ideas about infinities to people. Search for one of the other threads about this if you really care. Every point I could make has been repeated over and over again in them.

Also, to the OP: If you really wanted to get lots of views, you could have just made the title "FREE TITTIES INSIDE CLICK NAO!!1". It would have had about the same level of relevance to the content of the thread.

 

[Xirema]

It isn't, its just so close to 1 that nobody cares.

This is probably my biggest pet peeve, right next to people mixing up the usage of their/they're/there or your/you're.

0.999_ DOES equal 1. It's not "So close it doesn't matter", it's not "an infinitely small distance from 1", it's equal. Ask any professor of mathematics.

The reason people refuse to believe it is that they don't understand that numbers are symbols for man-made concepts, which means that there are discrepancies vis-a-vis the representation of the numbers. So you get weird stuff where 0.000_...1 is the same as 0, because 0.000_...1 is being used to describe a concept for which there's a poorly defined substitute in regular, base ten numeral representation.

There IS a branch of mathematics involving hyperreals (the name of which eludes me at the moment) that invokes this sort of nonsense where you have infinitely small numbers, or infinitely large numbers, but it doesn't work at all in the same way that defenders of "1 != 0.999_" would believe.

I'm sorry but .999... is not, nor ever will be equal to 1. Just think of it this is 1 = 2? no? well the same concept applies to this. 1 is not equal to .999... no matter how many 9s there are there will always just be a little bit missing.

Another way is to think about asymptotes in graphs.

Spoiler: asymptote

(this is just and image of a regular asymptote, not related to the scenario I'm explaining.)

Let's say that your asymptote boundaries are X=1 and y=1. That means that no matter how close to the boundary the line will get i.e. .999... it will never touch it because that will mean that 1 would be a solution to the equation of the graph, which for equations with asymptotes would not be possible because it would cause a 0 to appear in the denominator of the original equation. (equations that have asymptote have a variable in the denominator i.e. Y= 1/(X-1).)

Therefore .999... cannot equal 1.

That is not how math works.

 

[smallthemouse]

edit - nevermind read it wrong. 0.999repeating still evaluates to 1 though.

 

[Evil Smurf]

Edit to delete repeticious sentence.

I just threw forty-five dollars at my monitor and nothing is happening. Why has your math magic not started solving all my problems yet?

If you want all your problems to go away, you must first divide by 0.

no just alt+F4

......

hehe

 

[lacktheknack]

http://www.cracked.com/blog/6-innocent-sounding-topics-that-are-guaranteed-flame-wars/

Number 4 is going to happen again. You KNOW it will.

OT: 0.99999_ is functionally one.

It breaks reality if it isn't.

 

[Xirema]

http://www.cracked.com/blog/6-innocent-sounding-topics-that-are-guaranteed-flame-wars/

Number 4 is going to happen again. You KNOW it will.

OT: 0.99999_ is functionally one.

It breaks reality if it isn't.

Honestly? My complaint is now solely directed at your choice of the word "functionally", because, while you probably understand the concept, the people who don't (and refuse to understand it) are going to look at that and say "Oh, they're functionally the same, but not the same."

So I guess that was a self-fulfilling prophecy. XD

0.999_ and 1 are two ways of writing the same number. If I add 0.999_ + 0.999_ I expect the answer to be either 2 or 1.999_, both of which are also the same number.

 

[Feylynn]

Neat trick, sorry about that part where 0.999 people got it and the rest jumped straight to smashing your assumed physics revelation to pieces. =O

Reading, it's a virtue.
Or it should be.

 

[thethird0611]

I love this part of the wiki on .999_

"William Byers argues that a student who agrees that 0.999... = 1 because of the above proofs, but hasn't resolved the ambiguity, doesn't really understand the equation.[3] Fred Richman argues that the first argument "gets its force from the fact that most people have been indoctrinated to accept the first equation without thinking".[4]"

...Which is about the equation in the OP and the fraction 'answer'. Haha. I felt smart when I still argued in my head about it... then I felt dumb when I started reading more.

 

[lacktheknack]

http://www.cracked.com/blog/6-innocent-sounding-topics-that-are-guaranteed-flame-wars/

Number 4 is going to happen again. You KNOW it will.

OT: 0.99999_ is functionally one.

It breaks reality if it isn't.

Honestly? My complaint is now solely directed at your choice of the word "functionally", because, while you probably understand the concept, the people who don't (and refuse to understand it) are going to look at that and say "Oh, they're functionally the same, but not the same."

So I guess that was a self-fulfilling prophecy. XD

0.999_ and 1 are two ways of writing the same number. If I add 0.999_ + 0.999_ I expect the answer to be either 2 or 1.999_, both of which are also the same number.

I was trying to distance myself from the inevitable flame-war, but oh well.

Yeah, I retract my wording. 0.999... = 1.

COME AT ME BRO

 

[balanovich]

Alright, many of you have probably seen this before, but for those of you who haven't: get ready for some mathematical magic as I show you an old trick I learned back in highschool to algerbraeicly (spelling) prove that 0.999repeating actually = 1 by itself.

Start with x = 0.999rep

x = 0.999rep

Multiply both sides of the equation by 10

10x = 9.999rep

Subtract x from both sides.

9x = 9 (10x - x = 9x, 9.999rep - x (which was originally stated as = 0.999rep) = 9)

Divide both sides by 9

x = 1

You can also do this with fractions and logic.

1/3 as a fraction is equal to 0.333rep

2/3 as a fraction is equal to 0.666rep

3/3 as a fraction SHOULD equal 0.999rep....but as a fraction, having three thirds of something means you've got the whole thing, which equates to 1.



(on a side not...the Captcha required to post this contained the word "deleted" spelled backwards and upsidedown...what in god's name am I supposed to do there? (cycled through it) )

I hope you don't feel smart about saying what you just said... because it doesn't make you so. i bet you smoked weed an are in awe before the conflict with real numbers and irrational numbers.... "woow infinity stuff is awesome! I bet I can get people to think I'm smart." And I'm just flabbergasted (see, I toot can get people to think i'm smart.) by the way you failed to mention anything relevant to your title in your post!

 

[TriGGeR_HaPPy]

Oh god, this thread again. It's such an easy way to get a hundred pages of back and forth between those who understand complicated math and those who don't. I refuse to get sucked into another debate about this. It simply never ends.

Yes, .999... is exactly equal to 1. No, it does not involve rounding. They are exactly the same number. No, I'm not going to spend time explaining all of the different proofs and ideas about infinities to people. Search for one of the other threads about this if you really care. Every point I could make has been repeated over and over again in them.

Also, to the OP: If you really wanted to get lots of views, you could have just made the title "FREE TITTIES INSIDE CLICK NAO!!1". It would have had about the same level of relevance to the content of the thread.

This. Just this.
I mean, this thread has been repeated so many times, and as someone who's taken university level maths and talked to one of the heads of the maths department when I first found about about this (who talked me through various proofs for this, from the first one in the OP [worded slightly differently], right to using infinite geometric series for it)...

Just *sigh*.

However, what's with the title? Either you really don't know what this shows, or you just used this as an excuse to make a thread which will get lots of views and replies (and going by one of your own replies, yeah, it's the latter).
And hey, judging by the previous versions of this exact thread... You're almost sure to get just that. Sooo... Bravo, I guess.

 

[CAMDAWG]

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.

EDIT:

Oh yeah, and according to wikianswer matter can be created when gamma rays collide, or something like that.

Except that electromagnetic radiation has no mass. Newton's law of gravitation is at best an approximation. It works for objects on earth, and most planets, but can't handle mercury, let alone a black hole and/or light. For that you need general rel.

the fact that light is affected by gravity does not mean it has mass.