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Originally posted by metamagic
[snip] It's a basic exercise for first year students to show that... [snip]
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.
Originally posted by PhysicsAdept
reply to post by metamagic
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.
No, the z-score allows you to compare how something relates to something else, the weight of an apple compared to other weights below a normal curve vs. the the diameter of an apple compared to other diameters below a normal curve.
Originally posted by PhysicsAdept
reply to post by metamagic
No reference to Euler's formula at all.
Bull! The only reason why you can call e and pi real numbers are because of his formula, e^(pi*i)+1=0 !
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.
disprove it, go ahead. 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.
I would like to begin by saying that you have contradicted yourself here. you are saying that you see 1 apple because you have grown up with the CONCEPT of it being one apple but he is wrong because his CONCEPT of one apple is not exactly 1 because his math (statistics) , which is what he grew up with, tells him otherwise.
You are saying that concepts are bad because your concept disagrees with it, correct?
And you are saying you can find all of these things in concept, such as the area of a circle, but he is not allowed to find infinity as a number IN CONCEPT? If you are going to constantly tell someone they are wrong, and you give an example of their 'error', do not use the same error in your next post
It's a bit funny ain't it? He sits there and tells me that no one cares about the perfect apple and that we just group all apples into what tree they came from and then he goes on to tell me that a unit (here the unit is apple) is not a generalization itself.
1/infinity (limit- wise) approaches zero. Now, we keep talking about infinity. Some people here would argue that I speak of it as a number, I will not disagree with that here (though I merely believe it should be looked at as a plane, not a number itself.) but, you cannot refer to an infinity as a concept and then argue that 1/infinity does not equal zero. Because in concept, it very realistically will
Am I truly overthinking this? I thought I brought common sense into discussion. Thinking is a byproduct of discovery, perhaps some people on this thread have not yet discovered their own minds enough
Originally posted by OutKast Searcher
reply to post by ChemistryAdept
I would like to begin by saying that you have contradicted yourself here. you are saying that you see 1 apple because you have grown up with the CONCEPT of it being one apple but he is wrong because his CONCEPT of one apple is not exactly 1 because his math (statistics) , which is what he grew up with, tells him otherwise.
Everyone sees one apple. He is a classic example of overthinking himself into confusing himself.
I can have 2 apples...a small ripe red apple and a large unripe green apple...and I still have two apples. The unit of "apple" is defined by society...not by math. But still...if he wants to create his own unit of the "perfect apple" based on taking measurements and calculating the ideal size, weight, color, etc....that is fine. And then he can go through all the apples and find some "perfect apples". Those "perfect apples" will be a subset of the larger set of "apples".
But you can't take an apple and say "you don't have 1 apple there...you have half of a perfect apple because it's color isn't quite right". It just doesn't make sense. You can say, "That apple you have have is 50% perfect based on my criteria of a perfect apple." But the only way to have half of a perfect apple is to first find a complete perfect apple and cut it in half.
en.wikipedia.org...
Eleanor Roschis a professor of psychology at the University of California, Berkeley, specializing in cognitive psychology and primarily known for her work on categorization, in particular her prototype theory, which has profoundly influenced the field of cognitive psychology. Throughout her work Rosch has conducted extensive research focusing on topics including semantic categorization, mental representation of concepts and linguistics.. Her research interests include cognition, concepts, causality, thinking, memory, and cross-cultural, Eastern, and religious psychology.
From field experiments she conducted in the 1970s with the Dani people of Papua New Guinea, Rosch concluded that when categorizing an everyday object or experience, people rely less on abstract definitions of categories than on a comparison of the given object or experience with what they deem to be the object or experience best representing a category. Although the Dani lack words for all the English colors (their language contained only two color terms dividing all colors into either the 'light, bright' category or the 'dark, cool' category), Rosch showed that they could still categorize objects by colors for which they had no words. She argued that basic objects have a psychological import that transcends cultural differences and shapes how such objects are mentally represented. She concluded that people in different cultures tend to categorize objects by using prototypes, although the prototypes of particular categories may vary.
en.wikipedia.org...
Informally put, the axiom of choice says that given any collection of bins, each containing at least one object, it is possible to make a selection of exactly one object from each bin. In many cases such a selection can be made without invoking the axiom of choice; this is in particular the case if the number of bins is finite, or if a selection rule is available: a distinguishing property that happens to hold for exactly one object in each bin. For example for any (even infinite) collection of pairs of shoes, one can pick out the left shoe from each pair to obtain an appropriate selection, but for an infinite collection of pairs of socks (assumed to have no distinguishing features), such a selection can be obtained only by invoking the axiom of choice.
Malcontent mathematics instructor Feliz Raymond's afternoon naps are the subject of Rudy Rucker's strange and delightful White Light. Bored with his life and job at a state university in New York and making no headway in solving Georg Cantor's Continuum Problem, Raymond finds himself every afternoon, lying flat on his floor, entering into a state of lucid dreaming that allows him to explore an entirely new surreal and mathematically-charged reality. What follows is an adventure through time and space, the likes of which only a collaboration between Umberto Eco and Lewis Carroll could attempt. With traveling companions ranging from Einstein to the devil to a giant beetle named Franx, Raymond explores the infinite reaches of his new playground, which is filled with a multitude of cultural and scientific references, some subtle and many overt. Each turned corner of White Light is another gleeful surprise, another celebration of cleverness and imagination. Rucker, who is just as comfortable presenting accessible introductions to modern ideas in geometry (The Fourth Dimension: A Guided Tour of the Higher Universes) as he is spinning yarns of hacker fiction (The Hacker and the Ants), wrote this novel while, like the protagonist, endeavoring to solve Cantor's Continuum Problem at a state university in New York.
Originally posted by PhysicsAdept
People like you make people like me wish that websites like this never existed. No such thing as a think-tank. It is a myth apparently.
Originally posted by metamagic
Originally posted by PhysicsAdept
reply to post by metamagic
No reference to Euler's formula at all.
Bull! The only reason why you can call e and pi real numbers are because of his formula, e^(pi*i)+1=0 !
Euler's formula has (1) has nothing to do with the definition of pi or e, and (2) is a total red herring because it is a relationship between complex numbers not real numbers.
So then what are the definitions of pi and e? First of all the real numbers can be defined as the closure of the set of rational numbers. What that means is that when we have a Cauchy sequence of rational numbers (that is a sequence like [1/n] where the terms get arbitrarily close the further you go. Now the sequence [1/n] converges to [0] which is a rational number which is nice, but there are many sequences that don't. The set of all limits of all the Cauchy sequences of rational numbers is the closure of the rational numbers. So that means that e and pi can be defined as the limits of specific sequences of rational numbers. So here comes the fun part.
We can define e as the limit of (1 + 1/n) to the nth power as n approaches infinity.
Pi can be defined in terms of a simple continued fraction which is a number that looks like this
or in it's abbreviated notation.
So pi is defined as s.c.f to what is called the third convergent as
So that should pretty much eliminate the argument that the only reason e and pi are real is because of Euler's formula.
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.
disprove it, go ahead. 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.
No one said that number is not a limit, obviously every number x is the limit of the constant sequence [x,x,x,x,x...] But the question in mathematics is whether or not if we have a set of numbers N, the limits of the sequences of elements of N are also elements of N. For the rational numbers, the answer is no, for the real numbers the answer is yes.
Now everything after the question mark above has nothing to do with math, but is an expression of your personal beliefs about the nature of reality and how we use math to describe nature. I've only questioned the mistakes you have made in your description of math and statistics. The rest of it is a matter of your personal ontology.
Originally posted by ChemistryAdept
Layman's Terms it is....
Y=.0001X
Y=X^X
put this in your pretty little calculator and graph it.
which one grows faster? X^X. therefore it shall in concept reach infinity faster. By the time .0001X reaches this infinity then X^X is even BIGGER! Therefore it is at a bigger infinity!!! who would have thought that one infinity could be bigger!
Beyond that, infinity, as a numerical description can be applied somewhat in relativity. Involving the whole walk and run example, understand that both you AND I know that both distances equal infinity. the time it gets to reach this plane of infinity, NOT AN ACTUAL NUMBER (I get this even though you would swear up and down I do not) is much reduced from rate to another
I wanted a friendly exploration of infinity, and look. It has caused arguments that are getting nowhere. Where is the learning? I seek knowledge through discussion, not stagnation. If you do not wish to attempt in that endeavor, I am afraid I will not reply anymore.
Infinity, is it not there to represent those numbers we cannot count? We look to infinity to describe a concept of something that no one has yet actually encountered--which is everything.
People like you make people like me wish that websites like this never existed. No such thing as a think-tank. It is a myth apparently.
Originally posted by ChemistryAdept
reply to post by OutKast Searcher
Layman's Terms it is....
Y=.0001X
Y=X^X
put this in your pretty little calculator and graph it.
which one grows faster? X^X. therefore it shall in concept reach infinity faster. By the time .0001X reaches this infinity then X^X is even BIGGER! Therefore it is at a bigger infinity!!! who would have thought that one infinity could be bigger!
PS. about the apples, if you can generalize that an apple that fits 50% of the criteria is an apple, then why aren't you generalizing that an infinity small number is zero?edit on 18-3-2012 by ChemistryAdept because: Damn Typos...
Originally posted by Riakennor
Originally posted by ChemistryAdept
Layman's Terms it is....
Y=.0001X
Y=X^X
put this in your pretty little calculator and graph it.
which one grows faster? X^X. therefore it shall in concept reach infinity faster. By the time .0001X reaches this infinity then X^X is even BIGGER! Therefore it is at a bigger infinity!!! who would have thought that one infinity could be bigger!
There is a fundamental flaw in your logic here. One cannot 'Reach' Infinity. Infinity is boundless and has no end.
A bit like chasing the pot of gold at the end of the rainbow, you'll never get there, and the faster you move - the faster the pot moves