Matter /CAN/ be created!

[Maze1125]

As for the .9999 thing...... I don't see the relevance either. It's just a quirk of human, digital representation of the universe's analogue nature. It's a sampling error, if you like. One that gets ever smaller as you refine your digital representation to a more accurate level with more digits (same as sampling analogue data with more bits; something that would be 254.99609375 in a 16-bit system normalised to a 0-255 scale (or, 65279 without normalising) becomes quickly becomes 255 dead when you cut out some of the bits, especially when reducing to 8 bit. Similarly the universe holds 0.999 recurring to an infinite number of places; it trends to 1.0, but never reaches it. The limit here is one of our own perception, and of our number system. There could be room for a million and one 9's after the 0. when you spread your measurement out to encompass the planck length width of the entire universe, but if we only represent that with 999,999 nines, it becomes 1.0 ... the number under consideration hasn't changed, it's just that our representation of it is innaccurate.

You're right it's a quirk of our human representation, but you've got how the wrong way around.
It's not that the universe "knows" that 0.999... and 1 are different but we, as humans, misrepresent them as the same. It's that the universe "knows" that 0.999... and 1 are exactly the same number but we, as humans, have accidentally created a decimal system that can represent the same number in two different ways.

0.999... is just another way of writing 1.
1.999... is just another way of writing 2.
2.4572999... is just another way of writing 2.4573.
They are rather silly ways of writing those numbers, but they weren't invented to be useful, they weren't really invented at all, those ways of writing those numbers exist merely as a by-product of our number system.

 

[RJ 17]

Believe it or not, a quirk in maths that your teacher told you about in school does not equal a scientific breakthrough. This is worse than the responses to anything related to science by the Escapist newsroom, where a billion wannabe's cry out stuff that a scientist reppin' a PHD would have clearly already thought of.

snip

I lol'd.

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...

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.

To you three, I will direct you to a previous response of mine that should answer all your questions/concerns/irritation. This is simply an appeal to get people to lighten up a bit. I don't take myself seriously a good 85% of the time, neither should you all.

So... a misleading title to lead people into a thread where anyone who can understandthe topic already knows it, not to mention people (me) who've heard it, and simply accept it because they don't care enough about maths to consider it.

So... no discussion value, apart from pointing out that people who only use functional mathematics don't know complex mathematics, and that people will instinctively assume that numbers that aren't 1 aren't 1.

For the record, I've already been given my warning about having a misleading topic title. The reason I titled the topic as I did was specifically for the last part of your statement: to people not skilled in math, the 0.(infinite string of 0s)1 that makes 0.999_ = 1 seemingly comes from nowhere. However, as has been pointed out numerous times in this topic already: my math was flawed from the beginning. As for no discussion value, I beg to differ, as the topic has made it to 3 pages now.

But evidently some people just can't take a joke. Of course matter canNOT be created. If you honestly clicked on this topic thinking that you'd find some brilliant proof via ALGEBRA, of all things, that one of the most basic laws of physics is wrong, then I honestly feel sorry for you. (This being a message to everyone, not specifically the person I just quoted)

 

[Twilight_guy]

That has nothing to do with matter at all. Also, nuclear reactions can destroy and create matter by converting into into and from energy.

 

[Makhiel]

Oh my, should I tell the tale about the Hotel of Infinite Rooms to definitely screw with the minds of people who don't understand the OP's math? (Damn, I'm not trolling am I?)

 

[Weaver]

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

I'm with Mortai on this one. I have a degree in mathematics and this is no indication that matter can be created, it just means 0.9999... repeating is one. I don't know how one could really derive that this mathematical proof logically results in "we can create matter". It's nonsensical.

Allowing wiki to so kindly explain:
every nonzero, terminating decimal has an equal twin representation with trailing 9s, such as 8.32 and 8.31999... The terminating decimal representation is almost always preferred, contributing to the misconception that it is the only representation. The same phenomenon occurs in all other bases or in any similar representation of the real numbers.

This is like saying that F# and Gb are different music notes.

 

[oktalist]

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

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


Light has mass.

Light doesn't have mass. Newton's law of gravity is flawed. If light had mass and followed Newton's law, then it would be possible to change the speed of that light.

A massive object like a black hole causes the space around it to become curved, and light follows a straight line through curved space, so it appears to follow a curved line. When you get close enough to a black hole, the curvature is so great that light bends back in on itself.

3/3 does not = 1

Seriously?

To convince yourself of the cardinality problem, start with a finite number of digits and then extend the process by adding more digits. Keep going till you get to an infinite number of digits. You'll see that no matter how many digits you have, you always end up with an extra 0 after multiply by 10 and a remaining 1 after doing the subtraction in the last digit.

What.

Did you honestly write that with a straight face?

Because we use a number system based on 10, we cannot accurately measure things in thirds, so we use repeating decimals as approximations. Math is not a science as precise as you my think. .999rep is functionally equal to one, so mathematicians don't care. Your mistake is in assuming that 1/3=.333rep. It is not. That is an approximation of 1/3.

0.333... is not an approximation.
0.333 would be an approximation.
0.333... is exactly one third.
0.333 is exactly three hundred thirty-three thousandths.
0.999... is exactly one. Not just functionally equal, but actually equal.

Math is absolutely precise.

 

[geizr]

To convince yourself of the cardinality problem, start with a finite number of digits and then extend the process by adding more digits. Keep going till you get to an infinite number of digits. You'll see that no matter how many digits you have, you always end up with an extra 0 after multiply by 10 and a remaining 1 after doing the subtraction in the last digit.

What.

Did you honestly write that with a straight face?

Yes, I did. You do it abstractly. It's called a limit process. You do it all the time in Calculus to compute derivatives and integrals.

 

[irishda]

10x = 9.999rep

Subtract x from both sides.

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

No one else noticed that 10x=9.999r, when x is subtracted, DOESN'T equate to 9x=9?

Since x=.999r, the equation can also be written to equal .999r=.999r
Since the same thing is being applied to both sides (as it should with any algebra equation), OP's math should look like this.

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

or

x=.999r
10x=9.99r
10x-x=9.99r-x
9=9

OP only proved that a number equal to itself will turn out to be the same number.
Either OP's high school math teacher was a super awesome troll or had no business teaching algebra.

 

[oktalist]

Multiply both sides of the equation by 10

10x = 9.999rep

Fail Maths is Fail. You can't multiply an infinite by a finite.

What do you mean by "an infinite"? People multiply infinitely long numbers together all the time. Theres this thing called, Pi, you may have heard of it.

Given I did a degree in Maths, yes I did. What you may not know is that such numbers are called equivalencies and are used as approximations. 0.9Rep x 10 = 10 because that is the only way to get .9Rep. (It's an infinite approximation in itself ; An asymptote to give it it's contextual definition)

I'm surprised at you, Root. You are talking nonsense.

Finite and infinite do not mean what you think they mean in this context.

You can quite happily multiply rational and irrational numbers together: 2√2. That's not an approximation, that's twice the square root of two, written in exact form. 2.828 would be an approximation. But recurring decimals are rational anyway, so this isn't even relevant.

And an equivalency, if that were proper mathematical terminology, would not be an approximation, it would be an equivalency. I.e., something that is equivalent, the same, exactly equal.

What you may also remember from basic Trigonometry is that the radius and other calculations made from pi are rounded to the nearest two decimal places, because they are known to be inaccurate.

You can round it to as many decimal places as you think appropriate, or you can choose not to write it out as a decimal at all, and leave it in exact form. And calculating a radius isn't even trigonometry.

You may want to look up Calculus, Numerical Methods, Simultaneous Differential Equations

It's nothing to do with any of those things.

 

[geizr]

Because we use a number system based on 10, we cannot accurately measure things in thirds, so we use repeating decimals as approximations. Math is not a science as precise as you my think. .999rep is functionally equal to one, so mathematicians don't care. Your mistake is in assuming that 1/3=.333rep. It is not. That is an approximation of 1/3.

0.333... is not an approximation.
0.333 would be an approximation.
0.333... is exactly one third.
0.333 is exactly three hundred thirty-three thousandths.
0.999... is exactly one. Not just functionally equal, but actually equal.

Math is absolutely precise.

While you are correct that math is precise, Xiado is also correct that 1/3 cannot be precisely represented in base 10, just the same as 1/10 cannot be precisely represented in base 2. The problem isn't the mathematics, it's how you write the number, i.e. the representation. Again, if you do this as a limit process, you would find that no matter how many digits you add to the base 10 representation, the actual number would always require you to add at least 1 more digit to more accurately represent the number; in other words, the best you can do is to approach the number, asymptotically, but never actually reach it. Looking at the example of 1/3, in base 10, we need a zero followed by an infinity of 3s to asymptotically approach the value of 1/3. But, no matter how big the infinity of 3s we add, we will always need at least 1 more digit of 3; that is, we always need a, yet, larger infinity of 3s. However, as someone mentioned, if we switch to base 9, we can exactly represent 1/3 as 0.3, with no need for further digits.

The implication here is that there actually exists more numbers than we can represent solely in base 10, despite both sets being infinite in size. These kinds of difficulties arise because infinity is not the same size in all cases(just like the infinity of real numbers is bigger than the infinity of integers). That's why you have to consider the cardinality of the sets, which was the point I was trying to make in my post but likely failed to convey.

EDIT: minor edit for precision in first sentence.

 

[dyre]

heh, I remember when a friend showed this to me, and I thought it was pretty cool.....back in middle school. Also, not sure what the relevance to matter is :/

 

[Makhiel]

Looking at the example of 1/3, in base 10, we need a zero followed by an infinity of 3s to asymptotically approach the value of 1/3.

Which lucky for us, we can do. We just don't write it out and instead use a special symbol for it. Just like we can represent pi up to the "last" digit by simply writing the greek letter.

 

[ElPatron]

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.

I was thinking that OP never set foot in college, then you posted highschool maths.

I safely assume OP never set foot inside highschool, thank you.

 

[Tac0qvy]

Matter actually CAN be created. It takes energy.

E=MC^2

This Q&A answers it pretty well.


http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/970724a.html

 

[Bara_no_Hime]

**snip**

Um... of course you can create mater. You do so by converting the required amount of energy into matter. E=MC^2 works both ways.

I don't see how your math has anything to do with the creation of matter. All you proved is that there is no practical difference between 0.999_ and 1. And there isn't any practical difference between the two. However, that has nothing to do with matter, the creation of it or otherwise.

Edit: Ninjaed.

 

[oktalist]

To convince yourself of the cardinality problem, start with a finite number of digits and then extend the process by adding more digits. Keep going till you get to an infinite number of digits. You'll see that no matter how many digits you have, you always end up with an extra 0 after multiply by 10 and a remaining 1 after doing the subtraction in the last digit.

What.

Did you honestly write that with a straight face?

Yes, I did. You do it abstractly. It's called a limit process. You do it all the time in Calculus to compute derivatives and integrals.

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.

I've seen this trick a couple times, and it is incorrect because it breaks cardinality.

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

The key thing to realize is that infinity is not the same size in all cases.

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

When you multiply x=0.9999rep by 10, you have increased the cardinality by 1 with a hidden zero all the way at the end.

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

Thus, 10*x and x don't have the same cardinality.

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

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_root_of_all_evil]

I'm surprised at you, Root. You are talking nonsense.

You shouldn't be surprised. I talk nonsense some of the time.

None of the time with Maths though. You're getting rational/irrational numbers mixed up with finite and infinitely recurring decimals.

Any infinitely recurring decimal is, by definition, an approximation because there is no way to represent infinity, or an infinite recurrence, on a number line, except for an approximation.

If you want to disprove me, solve 1/0. Or x^3+y^3=z^3(xyz). Or the square root of -1.

And an equivalency, if that were proper mathematical terminology,

http://en.wikipedia.org/wiki/%E2%89%83
Asymptotic analysis. The terminology may have changed, the definition hasn't.
http://en.wikipedia.org/wiki/Congruence_relation
http://en.wikipedia.org/wiki/Approximation_theory
http://en.wikipedia.org/wiki/Diophantine_approximation

Please read up. This issue has been around for a lot longer than the 'net and has been "solved" many times.

 

[De_Roll_Le]

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.

Rabid Toilet is awesome.

 

[Axolotl]

What the fuck guys? Seriously what the fuck?

We've had this disscusion. It was long enough and stupid enough that it was used in a Cracked article. Seriously why the fuck are we doing this again. Nothing will be said that hasn't been said before.

It would be one thing if this were even something you could have an opnion on but no, it has a right answer and if you disagree with it then all the arguements and posts you can make won't stop you from being wrong. And it's even worse because the people being wrong pepper their nonsense with phrases along the lines of "Maths Fail!" and other self-congratulating pieces of inspid idiocy as if being wrong wasn't enough they have to be obnoxious about it as well. At last creationists generally admit their total ignorance.

Lok the OP is a either a troll (very likely)or by now has made it plenty clear they don't know what they're talking about. So please just walk away. If you really are deperate to know about 0.999 recurring equaling 1 then just go ask a maths professor I'm sure they'll be happy to explain and give proof.

 

[Vigormortis]

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.

I can explain all of this quite easily. Even using "layman's" terms.

Gravitation isn't just some magical attractive force. It's the curving of space/time. I'm sure I don't need to crack out the old bowling ball/rubber sheet analogy.

As such, regardless of whether something has mass, if it's in the presence of a gravity well it will inevitably fall towards the object creating the well. Ergo, light "bends" in the presence of gravity. This has nothing to do with light having or not having mass.

The equation you've listed is used to calculate the gravitation pull between two objects. Since light technically has no mass, it exudes no gravitation on the black hole. However, that does not stop it from reacting TO the black hole's own gravitation.

Oh, and as for the wikianswers thing....
It's a wiki-site. No matter what, take ANYTHING you find on those sites with a hefty dose of salt.

And gamma rays "colliding", or whatever the page was talking about, wouldn't "create" matter. What they were likely saying was that when the rays collide, the energy contained within the waves could be transformed into matter.

There is a difference.

I was going to type up a more specific, refined explanation, but Berenzen beat me to it.

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=m^2c^4 + p^2c^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.