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Math? Infinity and Zero (pg. 5)
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| Vizay |
ok after a nights sleep iv'e finaly came to the answer of the infinity problem...
it's not 0, it's not indeterminate (was that the word?)
The answer is!!! (insert snare here ;))
42
:D |
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| drizzt81 |
| quote: | Originally posted by Dmatrox
Zero times a # is: 0
Infinity times a # is: Infinity
So whats Zero times infinity?
1. Zero
2. Infinity
3. Somewhere in between? or ??
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ok, i have to solve the mystery. The 'number' infinity does not exist. Have you ever heard anyone say "some infinities are bigger than others!", well, if you haven't u now have. It is true, infinitiy is a concept, it is a limit.
one of the ways to get an answer being infinity, is to take the limit of a function.
Now, assume we have a function, f(x) = x * (1/x).
If you were to take the limit of this (x -> infinity), you would get infinity * 0, if you did it the WRONG way. but u can see that the powers of the variable are the same in numberator and denominator. Hence the answer is 1.
now let's say:
lim (x-> inf) f1(x) = 2x * (1/x)
this limit, again doing it the wrong way, you give you infinity * 0, but the correct answer is 2.
Anyhow, 0*inf, inf/0 and a couple more are called 'indeterminate forms' since you are unable to determine their values. this is different from undefined. Undefined means that there is NO WAY to compute this values. For indeterminate forms, you can.
If you get an indeterminate from, when taking teh limit of a function, you can apply L'hopitals rule and take the derivative of the numerator and devide it by the deriavtive of the denominator. The application of L'hopitals rule is denoted by an '*' above an equal sign.
After using this, you will get the correct limit!
Now let's look back at f(X) = x*(1/x)
we cna apply l'hopitals rule and say f(x) *= 1 * (1/1) = 1
similar for f2(x) = 2x * (1/x) *= 2* (1/1) = 2
look! it works. Now, these examples are AWEFUL. I am sorry, but i could not come up with a more interesting function.
Anyhow, this should answer your question about 0*infinity
and yes (infinity)^0 is also an indeterminate form :) |
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| astroboy |
| quote: | Originally posted by trancaholic
I hope this is not confusing anymore than what is inherent from the subject matter :) |
Sweet, that clears things up a bit. And I'm pretty sure you're right about things becoming more massive as they approach the speed of light, however I'm pretty sure I've also heard people say that photons have mass. :conf: :eyespop: |
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| trancaholic |
I dug out my trusty Serway's "Physics for scientists and engineers" (something I probably should have done earlier) and looked up mass and momentum for photons. It turns out that photons do not have mass, but they *do* have momentum. The momentum of a photon is its energy divided by the speed of light, c.
:) |
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| drizzt81 |
| quote: | Originally posted by trancaholic
I dug out my trusty Serway's "Physics for scientists and engineers" (something I probably should have done earlier) and looked up mass and momentum for photons. It turns out that photons do not have mass, but they *do* have momentum. The momentum of a photon is its energy divided by the speed of light, c.
:) |
of course they do, how would scientists otherwise use lasers to cool off atoms? I mean, we all know that the 'temperature' of an atom is caused by its movements. When they want to get an atom to be as close to 0K as possible, they cool it a lot and then they shoot a laser pulse at it. |
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| ali92 |
| quote: | Originally posted by drizzt81
of course they do, how would scientists otherwise use lasers to cool off atoms? I mean, we all know that the 'temperature' of an atom is caused by its movements. When they want to get an atom to be as close to 0K as possible, they cool it a lot and then they shoot a laser pulse at it. |
Is it possible to reach 0K, which is Absolute Zero? I heard that the deepest parts of space are around 3K and 1 000 millionths of a degree Kelvin have been possible in laboratory experients but, I never heard of ZERO being reached. Is reaching this temperature like reaching the speed of light, where no matter how fast ur accelerating, as you edge closer to that magic number (light speed) SOMETHING will slow you down? |
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| Dmatrox |
| when you say 0K do you mean -273 degrees |
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| Dmatrox |
| when you say 0K do you mean -273 degrees celcius |
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| ali92 |
| quote: | Originally posted by Dmatrox
when you say 0K do you mean -273 degrees celcius |
Yes... More precisely, I think it's -273.15 degrees Centigrade/Celcius or -459.69 degrees Fahrenheit. |
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| drizzt81 |
| quote: | Originally posted by ali92
Is it possible to reach 0K, which is Absolute Zero? I heard that the deepest parts of space are around 3K and 1 000 millionths of a degree Kelvin have been possible in laboratory experients but, I never heard of ZERO being reached. Is reaching this temperature like reaching the speed of light, where no matter how fast ur accelerating, as you edge closer to that magic number (light speed) SOMETHING will slow you down? |
it is not possible, since it would violate one of the laws of thermodynamics. and that is why i said 'as close to as possible' !! :D |
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| trancaholic |
| quote: | Originally posted by drizzt81
of course they do, how would scientists otherwise use lasers to cool off atoms? I mean, we all know that the 'temperature' of an atom is caused by its movements. When they want to get an atom to be as close to 0K as possible, they cool it a lot and then they shoot a laser pulse at it. |
Well, that effect really depends on momentum of photons rather than mass, right? You wouldn't expect something heavy to push something else, except if the heavy object was already travelling at some speed (that is, had momentum).
Accepting that a photon can have momentum, although no mass, can be difficult. But it might be easier if you interpret no mass, as litteraly "no mass" instead of "infinitely small mass", which is not necessarily the same things. The momentum of a photon stems from its energy rather than its mass, but when it collides with an object, the object doesn't care how that momentum came to be, it simply reacts to it. |
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| ABTsportsline |
I'd like to quote one of America's greats.
"In this house, we obey the laws of THERMODYNAMICS!"
-Homer Simpson.
:)
-ABT- |
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