Matter /CAN/ be created!
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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.thylasos said:
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)
Guess we haven't got many nuclear and/or particle physicists in this thread.
Matter is being created and destroyed at a high rate, constantly, along with antimatter. Electron-positron pairs pop in and out of existence all the time (they appear spontaneously, describe a mirrored arc thru space, and provided that nothing else interacts with one/other/both along the way, crash back into each other and annihilate in a puff of energy). Some radioactive materials chuck out a higher proportion of positrons (anti-electrons!) than most and this is the basis of the PET scanner - aka the Positron Emission Tomography machine.
That one is a natural occurrence. However it's entirely possible to generate matter by the input of energy to the right system (as someone else said on page 3, an exceedingly large amount of it - you would need as much to generate a gram of novel matter as would be released by annihilating a corresponding mass of matter & antimatter together. A well made bomb formed from that gram of stuff would make most thermonuclear weapons look like toys), though I conveniently forget what that is at this time
(It's been a while since I worked in the relevant field and i've got too many tabs open already to go dicking about in wikipedia, aight?)
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.
Inaccurate representations rarely lead to the creation of novel matter, unless we're talking metaphorically.
Matter is being created and destroyed at a high rate, constantly, along with antimatter. Electron-positron pairs pop in and out of existence all the time (they appear spontaneously, describe a mirrored arc thru space, and provided that nothing else interacts with one/other/both along the way, crash back into each other and annihilate in a puff of energy). Some radioactive materials chuck out a higher proportion of positrons (anti-electrons!) than most and this is the basis of the PET scanner - aka the Positron Emission Tomography machine.
That one is a natural occurrence. However it's entirely possible to generate matter by the input of energy to the right system (as someone else said on page 3, an exceedingly large amount of it - you would need as much to generate a gram of novel matter as would be released by annihilating a corresponding mass of matter & antimatter together. A well made bomb formed from that gram of stuff would make most thermonuclear weapons look like toys), though I conveniently forget what that is at this time
(It's been a while since I worked in the relevant field and i've got too many tabs open already to go dicking about in wikipedia, aight?)
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.
Inaccurate representations rarely lead to the creation of novel matter, unless we're talking metaphorically.
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.
I lol'd.chuckey said:
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.someonehairy-ish said:
You're right it's a quirk of our human representation, but you've got how the wrong way around.tahrey said:
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.
Woodsey said:
someonehairy-ish said:
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.burningdragoon said:
RJ 17 said: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.thylasos said:
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)
That has nothing to do with matter at all. Also, nuclear reactions can destroy and create matter by converting into into and from energy.
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.Mortai Gravesend said:
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.
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.triggrhappy94 said:
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.
Seriously?kaizen2468 said:
What.geizr said:
Did you honestly write that with a straight face?
0.333... is not an approximation.Xiado said:
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.
No one else noticed that 10x=9.999r, when x is subtracted, DOESN'T equate to 9x=9?RJ 17 said:
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.
I'm surprised at you, Root. You are talking nonsense.The_root_of_all_evil said:
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.
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.
It's nothing to do with any of those things.
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.oktalist said:
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.
