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Math? Infinity and Zero (pg. 4)
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| Arbiter |
| Just to further confuse matters, I'll throw in the fact that most mathematicians define infinity (whenever it is required for some particular application) such that infinity is not equal to infinity. :crazy: |
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| oDrori |
This is the most educative thread in TA history (Except that Extacy bible thing ;))
The time travel thing is really interesting!
Well, I don't know what to decide about the Infinity * 0 thing, I keep changing my mind ;) Though I do believe one Inifnity can be bigger than the other, theoretically:
You have 5*Infinity , and 4*Infinity . What I mean to say is that you have 2 infinite amounts of a unit, both uncountable, undefined etc. but the moment you have an amount of the first, you gotta have 4/5 of it of the other... (That made much more sense inside my head, hehe)
One more thing to ponder, this includes 2 points:
A. Acceleration is the rate at which Velocity changes, it is measured by units of velocity per units of time (m/s per second). Velocity is the rate at which distance changes, it is measured by units of disctance per units of time (m/s). What the is distance and what units-per-time does it use? (I know it doesn't but that's still a kind of a paradoxx)
B. Velocity, the rate at which distance changes is measured by units of distance per units of time (IE Meters per seconds = m/s). Acceleration, the rate at which velocity changes is measured by units of velocity per units of time
IE Meters-per-Second per Seconds = (m/s)/s = m/s/s = Meters per seconds per seconds
Working out some algebra, we see that a unit of acceleration is
M/S2 or Distance/Time Squared or Distance/(Time*Time).
What the f00k is time squared ?!?! |
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| infinity HiGH |
| quote: | Originally posted by Vanilla
I feel retarded by reading this thread and not understanding most of it. |
lol...i know! same here!
i was just telling my friend that i'm going back to looking at porn cause this is too mind-boggling for me |
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| trancaholic |
Infinity is not a number, and can not be used in equations without violating the equality implied by the equals sign. You might as well ask what the logarithm of a set is. No mystery, simply a nonsense question in a way.
Photons, according to classic physics theory, cannot have mass. When objects approach the speed of light, their mass increases very rapidly, and when their speed reaches light speed the mass would be infinitely big (actually meaning, if we choose an arbitrarily big mass, even the lightest object would reach this mass at some point on its way to lightspeed). The only possibility for a photon to have mass, would require it to have infinite mass and if that was the case, the photons reaching the earth from the sun, would push it out of the solar system.
If we instead turn to quantum mechanics/superstring theory (which is the best explanatory theory we have currently) things such as mass and lightspeed start to have different meanings. It's very complex and I won't go further into it, as I'm no expert at this.
For some really exciting reading on time travel, the possibility to distinguish a virtual reality from your own reality, and a host of other philosophical issues, you should chech out David Deutsch' "Fabric of reality". It is really good and non-dogmatic. |
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| Arbiter |
| quote: | Originally posted by trancaholic
Infinity is not a number, and can not be used in equations without violating the equality implied by the equals sign. You might as well ask what the logarithm of a set is. No mystery, simply a nonsense question in a way.
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That's not exactly true. Infinity is used frequently in mathematics, it just happens to be a member of the set of nonreal (aka imaginary) numbers, just like i. Numerous operations have been formally defined on infinity, whereas logarithms have not been formally defined on sets. |
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| astroboy |
| quote: | Originally posted by Arbiter
That's not exactly true. Infinity is used frequently in mathematics, it just happens to be a member of the set of nonreal (aka imaginary) numbers, just like i. Numerous operations have been formally defined on infinity, whereas logarithms have not been formally defined on sets. |
This is what was confusing me before. Why/how is infinity a non-real number? Can you explain? I learned some basic complex number stuff at school (but obviously we didn't learn anything too advanced like the nature of infinity). |
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| trancaholic |
| quote: | Originally posted by Arbiter
That's not exactly true. Infinity is used frequently in mathematics, it just happens to be a member of the set of nonreal (aka imaginary) numbers, just like i. Numerous operations have been formally defined on infinity, whereas logarithms have not been formally defined on sets. |
Imaginary numbers are the "numbers" needed for extending the real numbers to the complex numbers. Infinity is certainly not among the imaginary numbers, as they all are defined as ci, where c is in the real numbers and i is the square root of -1.
You're right that infinity plus a constant has been defined to be infinity, for example, but that's really just saying "whatever number you might come up with we can find something that is bigger" is the same as "whatever number you come up with we can find something that is bigger even if we have to add/subtract a constant". These definitions, however, do not allow you to use infinity as an unknown/a constant/a number in equations, if you want your restult to be mathematically rigorous (e.g. in research it's a big no-no). |
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| astroboy |
| quote: | Originally posted by trancaholic
Imaginary numbers are the "numbers" needed for extending the real numbers to the complex numbers. Infinity is certainly not among the imaginary numbers, as they all are defined as ci, where c is in the real numbers and i is the square root of -1.
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Yes this has also been the extent of my experience with imaginary numbers. Except I believ the form was either a + bi (the second term being the imaginary part), or cisin(theta) (commonly abbreviated cis(theta)).
However are you certain that this is the extent of the non-real set of numbers. For example (and I have no idea whether this contains so much as a grain of truth) it could be suggested that since infinity by definition contains all numbers, this must include those with imaginary or non-real elements making the whole entity of infinity non-real. |
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| trancaholic |
| quote: | Originally posted by astroboy
Yes this has also been the extent of my experience with imaginary numbers. Except I believ the form was either a + bi (the second term being the imaginary part), or cisin(theta) (commonly abbreviated cis(theta)).
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Yes, you're right except that they are called the complex numbers. The imaginary numbers would be the ones having b different from 0, or theta mod pi different from 0. Which is not exactly what I wrote in my previous post.:o
| quote: | Originally posted by astroboy
However are you certain that this is the extent of the non-real set of numbers. |
It is hard to say whether there are any non-real numbers different from the ones include in the complex number, as we might just invent such a number, say "ogo", which is not equal to any of the complex numbers, and thereby a non-real number as the real numbers are all included in the set of the complex numbers. However, how many properties we could prove ogo to have or define for it, is another matter.
| quote: | Originally posted by astroboy
For example (and I have no idea whether this contains so much as a grain of truth) it could be suggested that since infinity by definition contains all numbers, this must include those with imaginary or non-real elements making the whole entity of infinity non-real. |
When you say that infinity "contains" all numbers, what you mean is that no matter what number, c, you would compare to an entity having infinite value, c would be the smaller one. But as soon as we enter the realm of complex numbers, there can be no total ordering relation "<" (how would you judge whether 1-2i is bigger that 0+i for example). Since this ordering is what is needed in order to construct something that is greater than all elements in the set of numbers, I cannot see how it should be able to "hide", as a member of some of the number systems currently known/invented. Put that is no proof, and until someone comes up with a proof for either claim, we might as well call it a draw, and say either case is possible.
I hope this is not confusing anymore than what is inherent from the subject matter :) |
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| Dmatrox |
| quote: | Originally posted by oDrori
A. Acceleration is the rate at which Velocity changes, it is measured by units of velocity per units of time (m/s per second). Velocity is the rate at which distance changes, it is measured by units of disctance per units of time (m/s). What the is distance and what units-per-time does it use? (I know it doesn't but that's still a kind of a paradoxx)
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a = m/s/s
v = m/s
d = m
distance is not measured respect to time. distance is distance. When you travel you measure in distance (m), but if you want to know your velocity through your distance, you involve time ;) What im wondering is, whats after acceleration since a=m/s/s, so presuming the pattern, ?=m/s/s/s |
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| Dmatrox |
| quote: | Originally posted by trancaholic
Photons, according to classic physics theory, cannot have mass. When objects approach the speed of light, their mass increases very rapidly, and when their speed reaches light speed the mass would be infinitely big (actually meaning, if we choose an arbitrarily big mass, even the lightest object would reach this mass at some point on its way to lightspeed). The only possibility for a photon to have mass, would require it to have infinite mass and if that was the case, the photons reaching the earth from the sun, would push it out of the solar system.
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why would photons approaching the speed of light increase in mass? wouldnt it be logical for their mass to decrease?
Photons reaching earth from the sun wouldnt push earth out of the solar system because the gravitational attraction between the sun and earth and other planets is very very large compared to that of momentum of light.
As you said, photons cannot have light as defined by classical physics, but what about E=mc^2 where energy and mass energy is the equal of mass except for a conversion factor equal to the square of the speed of light. Where there is mass there is energy and wherever there is energy there is mass. |
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| trancaholic |
What E=mc^2 says is that the conversion factor between some mass and the energy it represents is c^2. Another result from classical physics say that the energy in the universe is always constant. It's just that some of it is bound up in mass.
Common sense would suggest that if an object was continually being accelerated, it would sooner or later reach the speed of light and a little later be even faster. The speed of light can, however, not be surpassed (something to do with the way light travels in jumps or something) and the energy applied to the object as it gets closer to lightspeed must thus be used for something else. As all kinds of energies are basically the same, it cannot go into heat, electricity etc. so instead it is converted into mass that instantly attaches to the object due to gravitational force. Hence the object becomes heavier, and if continued acceleration is present it will be heavier and heavier without ever reaching lightspeed. Notice that this happens no matter how minuscule the mass of the initial object is. So if a photon had mass, it could never be accelerated to lightspeed.
As stated I'm not an professional physicist, so my info might be error-ridden, and I urge you to go check it out yourself.:) |
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