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2. The stuff about z-scores and variance measures is gibberish. A z score is used to transform an arbitrary NORMAL distribution to a standard normal distribution mean mean=1 and s.d. = 1.
It's not beside the point, it IS your point. You are assuming a normal distribution.
I disagree with all three of your points
A unit is not a generalization...it is a unit. You apple example is just flat out wrong...because no one says I have 3 perfect apples...they just have 3 apples. The "normalcy" of the apple doesn't matter...all that matters is that it fits the minimum definition of an "apple"...which is not mathematical at all. Same thing if you are counting cars, or clouds, or basketballs. A better example for you to have used is units of measurment...because there is no exact "inch" or "centimeter". So you could argue that something is never exactly an "inch" long...but you can't say you can never have exactly 3 apples. You could say you can never have 3 "perfect apples" as defined by size, color, smoothness, luster, taste, nutritional value, etc. But just using the generic unit of "apple" has not other mathematical criteria rather than the fruit you are counting to be defined as an "apple".
Each data point does not have an area of zero. It has an area that approaches zero...but it is never zero. It can have an area of 1 if you use some imaginary unit of measure that signifies a very very small area. Or it can have an area of 10^-1000000000000000000000 mm^2. But it will never ever have an area of zero. If you divide into infinite points, than the area of each one could be described as the inverse of infinity...or you can say it is infinitely small...but not zero.
Infinity is a concept. The "infinity" between 1 and 2 is the same as the "infinity" between 1 and infinity. That is why infinity is a concept and not a number. When you start saying one is larger than the other, you are changing the definition.
What do you mean by perfect? In fact you seem to be saying that graphs are close approximations ("the closest you will ever get to a circle that equals pi" -- although it makes no sense to say that a circle equals pi). I would argue that graphs are horrible imperfect. A line has no width yet any depiction of a line has width.. imperfect by my definition.
False, the graph may draw the line, but the graph itself is showing only what you would perceive it to be. When that stuff happens in nature, it only happens as concept, as nothing in nature is truly 2-dimensional. However, rates CAN be. You cannot SEE the thickness of a rate can you? Yet, the graph will show thickness to it, zoom it, I dare you to tell me that line gets thicker.
No reference to Euler's formula at all.
Which is pretty much a total misunderstanding of what a limit and number are. My suggestion is that if you want to publicly use mathematical terms and concepts, take the time to learn what they are. It's actually very interesting.
Wait a sec, you are saying already that you disagree with it being a generalization because... wait, because "no one says I have three perfect apples"? CORRECT, no one is not! They are generalizing that you have apples. The apples you would then hold in your hand, all three of them would be different. You are generalizing them by specifically suggesting they are the same in concept. If you told me those apples were all exactly the same, that would not be a generalization now would it? It would be saying that they are all the same. The math comes into play here, because it is nearly impossible to say that they are all the same, each one will have a flaw that another one will not or that will be flawed differently. So instead, you generalize them. You say that you have three apples, and imply that "minimum definition of an "apple"". Don't even try to refute this... you agree with me without even understanding why, you just want to argue...
Maybe you have taken an advanced math class, but here would prove to me that you have not. in math, a basic concept is that when you take a limit of something, 1/infinity is equal to 0.
SO I just proved that you are correct using basic calculus, yet here is where even this logic can not make any sense. You do know that there are an infinite amount of points in that circle right? So I broadly stated that you add up a bunch of zero an infinitely large amount of times to get pi, correct? So now, you are reminding us that we actually are adding up more than zero an infinite number of times? So now it looks like my point of this whole thread has been reached! You end up getting a pi unit of infinity! Thanks!
Sigh... perhaps you should just reread my post. You seem to have gotten nothing out of what has been said. I will just do what you do in a majority of your posts and say, prove it.
Not trying to be mean, really I apologize if I am coming off that way. I merely wish for things to be carefully understood before posting. I get that I suck at getting out what I am trying to say, but now you have to math. Research it all you want--you will find out that I am not wrong numerically
How is a number not a limit in and of itself? Because there can never exist perfection in nature that accurately resembles itself as being EXACTLY 1, when we use the number 1 we are referring to the approximation, or generalization of its value. In all likelihood, 1 in nature would really compute to a value of 1.000000000000000000000000000001 in whatever we were determining... You guys really are not getting this post. Confusedly too, seeing as you are obviously very intelligent.
Originally posted by OutKast Searcher
reply to post by PhysicsAdept
How is a number not a limit in and of itself? Because there can never exist perfection in nature that accurately resembles itself as being EXACTLY 1, when we use the number 1 we are referring to the approximation, or generalization of its value. In all likelihood, 1 in nature would really compute to a value of 1.000000000000000000000000000001 in whatever we were determining... You guys really are not getting this post. Confusedly too, seeing as you are obviously very intelligent.
You can't tell the exact length of a string in real life...you can never know the exact area of a circle in real life...but you can in concept.
But you can know you have 1 apple. You may not be able to know you have a specific weight of an apple...but you have 1 apple because we have defined an apple to mean something that is only dependent on a few specific details.
Originally posted by Riakennor
I find Infinities very intriguing. Although in themselves they are only theoretical.
In the real world, they do not and cannot exist. Right ?edit on 17-3-2012 by Riakennor because: (no reason given)
Originally posted by PhysicsAdept
If I told you to count particles in the universe, you may think of a million, or total photons the sun has radiated from its birth and you would say it is such a large number that really it is infinite.
Originally posted by PhysicsAdept
as I have said, there are some infinities that are just much larger than others (in concept)
The truth is, everything that exists, pretty much, can be calculated. Humans put labels on things they cannot, or rather are afraid, count.
Originally posted by PhysicsAdept
Even if we had a true sphere, with radius of 1-meter, it (might) exist in space under an infinite amount of points, just as on paper with a circle. So then we have a a body, or "system" of 4pi/3 meters^3, which is an finite number of points in space. This system, however, is much less than a sphere of say 100 meters radius. It also has perhaps an infinite amount of points in space, yet obviously many more points than with radius of 1.
See where I am going?