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Originally posted by FabianFnasI think of a real number. What is the probability that you can guess this number? P(You can guess exactly that number)= Zero, of course.
I read it, I understand it, but I don't havethe same interpretation.
Perhaps we should lift it up a lever. Let my teacher and your teacher debate this instead of us two?
What is a probability that a human being has exactly my length? One. Because here I am!
What's the probability that another one have the same length that I have? Zero. (Unless you don't think about the trick question.)
None of this is relevant to the interpretation of a 0 probability in the context of continuous variables.
Perhaps we should lift it up a lever. Let my teacher and your teacher debate this instead of us two?
And as a third option I suggest you to talk to your teacher so that he can teach you these things again. Cause I don't need anyone to take my place in this discussion.
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Originally posted by KazetNagorraI deserved that one:
One who knows that a L = 0 box doesn't allow any EM mode. 😉
1 - I think it's obvious that I intended to write L being finite since I replied to your post
2- Since we were discussing probability = 0 I wrote L = 0.
Shame on me for not proofreading and shame on me for bumping without proofreading.
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Originally posted by FabianFnasAnd before you were born what was the probability of an human being having exactly that length at the timestamp of your post?
I read it, I understand it, but I don't havethe same interpretation.
I think of a real number. What is the probability that you can guess this number? P(You can guess exactly that number)= Zero, of course.
What is a probability that a human being has exactly my length? One. Because here I am!
What's the probability that another one have the same l we should lift it up a lever. Let my teacher and your teacher debate this instead of us two?
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Sorry to bring this up yet again but I am just still totally stuck:
At: http://en.wikipedia.org/wiki/Planck's_law
And many similar websites it uses the mathematical notation to the left of the equal’s sign in the general form: “A( B, C ) =….” -but the problem is I don’t undestand what this “A( B, C )” means. For example, at http://en.wikipedia.org/wiki/Planck's_law it says: “I (v, T ) =…” in its first stated equation and, although I know what “I” and “v” and “T” means, I don’t know what “I (v, T ) =…” means. Can anyone explain to me what it means or give me a link that explains that mathematical notation?
Also, for a given temperature T, I want to simply plot a curve on a graph with power radiated (in joules per second and power radiated in all directions) from a perfectly flat one metre squared area of solid black surface at that given temperature T (that behaves like a perfect black body) represented along the vertical axis of the graph and either wavelength or frequency (don’t care which) represented along the horizontal axis of the graph (so each point on that curve represents the total power (joules per second) radiated from that flat surface at a particular wavelength/frequency and so the area under the plotted curve represents the total joules per second radiated away from that perfectly flat one metre squared area of solid surface at that temperature T).
-which equation should I use for this and how?
Originally posted by Andrew HamiltonFor that you simply use the function I(v,T). I(v,T) dv represents the power density over the frequency interval dv. So if you want to know the radiated power over a certain frequency interval you integrate over the interval. If you want to know the total power emitted at a certain temperature T, you can either integrate over all v, or simply use the Stefan-Boltzmann law.
Sorry to bring this up yet again but I am just still totally stuck:
At: http://en.wikipedia.org/wiki/Planck's_law
And many similar websites it uses the mathematical notation to the left of the equal’s sign in the general form: “A( B, C ) =….” -but the problem is I don’t undestand what this “A( B, C )” means. For example, at http://en.wikipe ...[text shortened]... area of solid surface at that temperature T).
-which equation should I use for this and how?
http://en.wikipedia.org/wiki/Stefan-Boltzmann_Law
Originally posted by Andrew HamiltonIt means that the intensity has a dependence in the frequency of the radiation emitted and it also depends at what temperature the black body is radiating.
Sorry to bring this up yet again but I am just still totally stuck:
At: http://en.wikipedia.org/wiki/Planck's_law
And many similar websites it uses the mathematical notation to the left of the equal’s sign in the general form: “A( B, C ) =….” -but the problem is I don’t undestand what this “A( B, C )” means. For example, at http://en.wikipe ...[text shortened]... anyone explain to me what it means or give me a link that explains that mathematical notation?
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Originally posted by adam warlockI am having some difficulty thinking clearly about this:
It means that the intensity has a dependence in the frequency of the radiation emitted and it also depends at what temperature the black body is radiating.
does this mean I could rewrite any equation that starts with the general notation:
“A( B, C ) =….”
As simply:
“A =….”
-without changing the right-hand side and it would still make perfect sense (by being correct)?
And if I rewrite:
“I(v,T) =….”
As:
“I(T,v) =….”
-without changing the right-hand side then would that still make perfect sense (by being correct) and with the SAME meaning?
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Originally posted by Andrew Hamilton...for a given temperature T, I want to simply plot a curve on a graph with power radiated (in joules per second and power radiated in all directions) from a perfectly flat one metre squared area of solid black surface at that given temperature T (that behaves like a perfect black body) represented along the vertical axis of the graph and either wavelength or frequency (don’t care which) represented along the horizontal axis of the graph (so each point on that curve represents the total power (joules per second) radiated from that flat surface at a particular wavelength/frequency and so the area under the plotted curve represents the total joules per second radiated away from that perfectly flat one metre squared area of solid surface at that temperature T).
Also, for a given temperature T, I want to simply plot a curve on a graph with power radiated (in joules per second and power radiated in all directions) from a perfectly flat one metre squared area of solid black surface at that given temperature T (that behaves like a perfect black body) represented along the vertical axis of the graph and either wa ...[text shortened]... ed area of solid surface at that temperature T).
-which equation should I use for this and how?[/b]
-which equation should I use for this and how?
...
-Anyone?
-this is the question I would really most like to know the answer to and I would greatly appreciate any help.
Originally posted by Andrew HamiltonYes to both questions.
I am having some difficulty thinking clearly about this:
does this mean I could rewrite any equation that starts with the general notation:
“A( B, C ) =….”
As simply:
“A =….”
-without changing the right-hand side and it would still make perfect sense (by being correct)?
And if I rewrite:
“I(v,T) =….”
As:
“I(T,v) =….” ...[text shortened]... hand side then would that still make perfect sense (by being correct) and with the SAME meaning?
Originally posted by Andrew HamiltonNotation is just notation. You can label anything with whatever you want.
I am having some difficulty thinking clearly about this:
does this mean I could rewrite any equation that starts with the general notation:
“A( B, C ) =….”
As simply:
“A =….”
-without changing the right-hand side and it would still make perfect sense (by being correct)?
And if I rewrite:
“I(v,T) =….”
As:
“I(T,v) =….” ...[text shortened]... hand side then would that still make perfect sense (by being correct) and with the SAME meaning?
Usually people stay with conventional notation just for convenience. If it becomes more convenient to change it, then there's no reason why not. Just remember to keep track of what you're doing.