1=.999999...?

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Re: 1=.999999...?

Postby Wonderer » Fri Jun 27, 2008 5:35 pm

Aidan_Mclaren wrote:Do you really see fruit being bared, or do you pretend to see it?


Go pick the fruit from your other threads please, this is a math thread.
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Re: 1=.999999...?

Postby Aidan_Mclaren » Sat Jun 28, 2008 12:58 am

Can't I respond to Juggernaut's post that is also irrelevant (yet I don't see you picking at him)?

Please shut up, Wonderer.
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Re: 1=.999999...?

Postby Juggernaut » Sat Jun 28, 2008 3:37 am

Aidan_Mclaren wrote:Can't I respond to Juggernaut's post that is also irrelevant (yet I don't see you picking at him)?

Please shut up, Wonderer.

Address the great Juggernaut, lord of the universe by name if thou wishes to banter about with him. You many be too sharp for his sensitive tastes, or he may just be out picking his strawberries while the mosquitos feed upon him. Who exactly knews?
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Re: 1=.999999...?

Postby Aidan_Mclaren » Sat Jun 28, 2008 4:23 am

I thought we already did.
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Re: 1=.999999...?

Postby Juggernaut » Sat Jun 28, 2008 12:16 pm

Aidan_Mclaren wrote:I thought we already did.

The number you have dialed is not in service. Please hang up and try again.
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Re: 1=.999999...?

Postby Wonderer » Sat Jun 28, 2008 8:02 pm

Aidan_Mclaren wrote:Can't I respond to Juggernaut's post that is also irrelevant (yet I don't see you picking at him)?

Please shut up, Wonderer.


Both of you can take this shit hole of a discussion out of this thread please and thank you.
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Re: 1=.999999...?

Postby Juggernaut » Sat Jun 28, 2008 9:20 pm

If the rigors of defining one thing apart from another is beyond your ability, try something else. To me, that is what philosophy is about, and not whether math follows the rules it sets for itself. From a practical point of view .99 is one, and to arrive at that part of one in reality is difficult unless beginning with an arbetrarily arrived at one, such as 1=100. But, there is always a certain benefit from imagining smaller and smaller graduations of matter because that is the route from which finer and finer measuring devices have come. If some guy can drive by my house and measure from his vehicle the charge given off by a piece of sacrificial anode buried eight feet under the ground to protect the gas line from corrosion, it is an ability that grew out of some ones brain, and a fine conception of reality. If I may give you an example it would be this. Like many people before and during his age, Galileo considered acceleration as change of speed over distance, as opposed to change of speed over time. Considering the age in which he lived, what alternative was there, since there was no means of graduating time to such a degree as to make that progress of understanding possible, and only with time and growth did he change his understanding, and this was a great advance for physics. Physical progress is a step by step process with our ability to measure adding to our understanding, and our understanding adding to our ability to measure, and again from measurement to greater understanding. The difference between .999 bar and one may be a hair's breadth, if that; but only by considering it will we ever be able to measure it. Thanks
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Re: 1=.999999...?

Postby Wonderer » Sat Jun 28, 2008 9:30 pm

Juggernaut wrote:If the rigors of defining one thing apart from another is beyond your ability try something else. To me, that is what philosophy is about, and not whether math follows the rules it sets for itself.


I really do respect that, but not in my math thread in the natural sciences section :wink:

This thread has a clear and consice aim. You and Aidan are kind of wrecking it by continuing a conversation which serves your desires, and not the desires of the thread.

cheers.
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Re: 1=.999999...?

Postby Juggernaut » Sat Jun 28, 2008 9:58 pm

Wonderer wrote:
Juggernaut wrote:If the rigors of defining one thing apart from another is beyond your ability try something else. To me, that is what philosophy is about, and not whether math follows the rules it sets for itself.


I really do respect that, but not in my math thread in the natural sciences section :wink:

This thread has a clear and consice aim. You and Aidan are kind of wrecking it by continuing a conversation which serves your desires, and not the desires of the thread.

cheers.

I have given up on the truth always being true, but short term, math should agree with language, and be logical, and though we assume that of math it is hardly proved. I try to look at reality in microscopia, and also get the big picture, because when I judge our abstractions I find they must be true to reality. And numbers are fine, for representing a finite reality. I see little practical point in figuring pi out endlessly if no perfect circle can be produced in reality, so what is the point of a concept that is more perfect than reality? Surely you would agree that a .999... one is more difficult to work with and time consuming, and so contrary to the purpose of math which is to ease thought and calculations; n'est pas?
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Re: 1=.999999...?

Postby aporia » Sat Jun 28, 2008 10:42 pm

I see little practical point in figuring pi out endlessly if no perfect circle can be produced in reality, so what is the point of a concept that is more perfect than reality?


I wouldn't describe a mathematical circle as more "perfect" than a physically realized one, whatever that may mean. But a mathematical circle is easier to describe mathematically than a real circle, whose bumps and jitters would require a great deal of mathematical complexity to account for. The point of the mathematical world is not that it is more ideal or perfect, but that it is simpler. It picks out the important patterns we see in the real world and makes simple models of them, so that it is possible to construct more complicated but still understandable models of reality.



Surely you would agree that a .999... one is more difficult to work with and time consuming, and so contrary to the purpose of math which is to ease thought and calculations; n'est pas?


.9[bar] = 1 in itself may not make anything easier to understand or calculate. But in other situations, it IS easier to work with an infinite series than with the number it converges to. In fact, sometimes the only formula we have for the number is an infinite series (the number e is an example). The same principles that allow you to work with such numbers tell you that .9[bar] = 1. So if you throw out .9[bar] = 1, you throw out those principles, and you throw out your ability to work with those infinite series. Then you lose your ability to understand many important equations of physics, because many of their solutions are known only as infinite series.

I can understand the difficulties people are having with .9[bar] = 1 in this thread. But denying .9[bar] = 1 is really a classic case of throwing the baby out with the bathwater. So much of physics relies on limits and infinite series to create simplified models of reality that are mathematically understandable and solvable. It's paradoxical that solving a problem with an infinite series can make things simpler than working with a finite sum. But it happens very often.
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Re: 1=.999999...?

Postby Juggernaut » Sun Jun 29, 2008 2:53 am

aporia wrote:
I see little practical point in figuring pi out endlessly if no perfect circle can be produced in reality, so what is the point of a concept that is more perfect than reality?


I wouldn't describe a mathematical circle as more "perfect" than a physically realized one, whatever that may mean. But a mathematical circle is easier to describe mathematically than a real circle, whose bumps and jitters would require a great deal of mathematical complexity to account for. The point of the mathematical world is not that it is more ideal or perfect, but that it is simpler. It picks out the important patterns we see in the real world and makes simple models of them, so that it is possible to construct more complicated but still understandable models of reality.

Well; mathematical circles are perfect, but untrue since, in reality all circles are only circular. But, we cannot improve upon nature, but only understand nature by way of perfect models. Ideals are ideal. The conceptual apple, which is an ideal apple contains every quality of all apples even while every apple is different, because no apple is so different as to not be an apple were it not perfect in this regard, and complete, it would not as a concept define all apples. Math is an abstraction of reality, and as such one is always one, where as, in nature no two ones are equal, qualitatively, and so cannot equal togther any other two. What Aristotle said of each number being in ratio to the others, is not true of units in nature, and which from our perspective has a qualitative meaning rather than a quantitative meaning. Math as strictly quantitative, and in always keeping a perfect ratio of one with other numbers is unreal, and perfect.


Surely you would agree that a .999... one is more difficult to work with and time consuming, and so contrary to the purpose of math which is to ease thought and calculations; n'est pas?


.9[bar] = 1 in itself may not make anything easier to understand or calculate. But in other situations, it IS easier to work with an infinite series than with the number it converges to. In fact, sometimes the only formula we have for the number is an infinite series (the number e is an example). The same principles that allow you to work with such numbers tell you that .9[bar] = 1. So if you throw out .9[bar] = 1, you throw out those principles, and you throw out your ability to work with those infinite series. Then you lose your ability to understand many important equations of physics, because many of their solutions are known only as infinite series.

Which physics problems that you know of depending upon an infinite series for their solution. Please; and since we cannot produce an infinite in reality, how can we know that the answer holds? Let me tell you a part of the problem, as I see it, though I have touched on it. For anything to be said to equal one, one must be defined as one and nothing other. Part of the definition of one is the ratio of one to all other numbers as I mentioned. Now; one is easily defined, and so is the essential concept of math. And since it is in ratio to all other numbers, it is one alone -which defines them. So if we say: The ratio of one to two is twice as great as the ratio of one to four, and so on and on, then this is a constant, by way of definition. To decide if .999 bar is the same as one, we need to actually compare the ratio of one to two, with the ratio of .999bar to two, and four, and eight, and etc. Because by axium, one is half of two, but also only equal to one, so that by definition .999Bar is excluded on the one hand and not proved on the other. Putting math tricks based upon unfinished, and unsolved problems does not make .999Bar equal anything, because it must be something, that is, complete, and finite before it can be counted. Does that make any sense to you?
I can understand the difficulties people are having with .9[bar] = 1 in this thread. But denying .9[bar] = 1 is really a classic case of throwing the baby out with the bathwater. So much of physics relies on limits and infinite series to create simplified models of reality that are mathematically understandable and solvable. It's paradoxical that solving a problem with an infinite series can make things simpler than working with a finite sum. But it happens very often.

Let me agree that math does not need to be perfect to shed some light on reality, but it makes the claims for itself when it says one is one, and one and one are two every single time. In fact we have seemingly infinite series in the rotation of the earth, but reason says it is not infinite and science proves it is not. We can imagine an electron cloud in seemingly endless repetition and variation about an atom, but we know all atoms decay sooner or later. So short term, if we treat nature as infinite we can explain certain behaviors of matter in physics, but we must tell a little fib to get there. This does present a little ontological question of: Do we really know it?
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Re: 1=.999999...?

Postby aporia » Mon Jun 30, 2008 6:46 pm

Juggernaut

Which physics problems that you know of depending upon an infinite series for their solution


Well, the trigonometric and exponential functions cannot be computed without the aid of infinite series. For example your calculator automatically determines how many terms to use in the infinite series to guarantee a certain degree of accuracy according to limit theory, and then computes that number of terms.

Bessel functions are given as infinite series, and they are used to describe such diverse physical phenomena as heat and wave propagation, the vibration of a drum, and electronic orbital wave functions.

To decide if .999 bar is the same as one, we need to actually compare the ratio of one to two, with the ratio of .999bar to two, and four, and eight, and etc. Because by axium, one is half of two, but also only equal to one, so that by definition .999Bar is excluded on the one hand and not proved on the other. Putting math tricks based upon unfinished, and unsolved problems does not make .999Bar equal anything, because it must be something, that is, complete, and finite before it can be counted. Does that make any sense to you?


Not really. You claim that .9[bar] is "excluded by definition" somehow but don't show why. As for .9[bar] needing to be complete and finite before it is "counted" (presumably you mean before it is a number)... well according to limit theory .9[bar] is a number. It is the number approached by the sequence (.9, .99, .999...) as I discussed with Wonderer. 0.9[bar] is NOT a sequence or a process or approaching anything. It is a number approached BY the sequence (.9, .99, .999...) by definition. Disputing whether such a number can exist will not help you; the number can be mathematically constructed and proven to satisfy the ordinary arithmetic properties, as well as .9[bar] = 1.

Let me agree that math does not need to be perfect to shed some light on reality, but it makes the claims for itself when it says one is one, and one and one are two every single time. In fact we have seemingly infinite series in the rotation of the earth, but reason says it is not infinite and science proves it is not.


What? How is there an infinite series in the rotation of the earth? Do you mean that it seems like it will go on forever?

One can mathematically model the earth's rotation as though it would be constant and eternal; this is a simplifying approximation which allows for effective modeling. Adding in all the little messy details of reality would make higher modeling impossible, losing sight of the forest for the trees.

We can imagine an electron cloud in seemingly endless repetition and variation about an atom, but we know all atoms decay sooner or later. So short term, if we treat nature as infinite we can explain certain behaviors of matter in physics, but we must tell a little fib to get there. This does present a little ontological question of: Do we really know it?


It's not a fib, it's a nonexact approximation which is known to be a nonexact approximation. An approximation, like any scientific theory, is verified by empirical success and theoretical coherence. For example, we can theoretically show that the earth's decay in rotation speed is very slow relative to any experiment we might do measuring its rotation rate. So we can approximate its rotation rate as constant. Then we can test that approximation in various experiments. If the approximation is close to reality in a precise sense given by limit theory, then the approximation is vindicated as being essentially correct.

Let me break it down step by step.

If you want to make mathematical models of physical reality that generate testable predictions, you must create simplified models that approximate unknown or difficult-to-calculate quantities in various ways. And you need to have some way of knowing your approximations are close (else if the experiment fails, you don't know if it's because your approximation was bad, the theory's wrong, the equipment setup is bad, or some other reason). If you want to understand how to approximate an unknown quantity and be sure that you're close, limit theory is a very powerful tool for doing that. And once you have limit theory, you have 0.9[bar] = 1.

Maybe there is another way to do approximation theory besides limits, but I highly doubt it. Don't knock it until you try it.
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Re: 1=.999999...?

Postby Aidan_Mclaren » Tue Jul 01, 2008 3:32 am

So by that, you admit "0.999 recurring equals 1" is a logical shortcut?
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Re: 1=.999999...?

Postby Juggernaut » Tue Jul 01, 2008 4:20 am

Aidan_Mclaren wrote:So by that, you admit "0.999 recurring equals 1" is a logical shortcut?

It's a shortcut, and if math is logical, then what math presents as true, is logical. Math may presume such an equality between .999 recurring, and one; but if it cannot produce a finite example of it they can hardly prove it, or equally important, show the ratio between .999 recurring, and two; is the same as the ratio one to two. And etc. If the number works to explain some phenomena, then it has some support short of proof. If .999 recurring is just a figure inserted some place to make equasions work, then they really don't teach anything new, and something, in fact very old. It is like the Ptolemaic universe, Math in the service of a prejudiced truth.
What I said before about the definition of one, means that the identity of anything defined is conserved. A cat is a cat if shaved hairless, or declawed, or neutered. Its definition establishes it as an identity unlike any other. What is the identity of one? It will either be 1, or .999 recurring; and not both, or something else. No thing can be truly this or that, and neither can one. It in some respects is the difference between being and becoming. One can be one, and perhaps .999 recurring can become one; but until it does, it is not one.
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Re: 1=.999999...?

Postby aporia » Tue Jul 01, 2008 2:51 pm

Math may presume such an equality between .999 recurring, and one; but if it cannot produce a finite example of it they can hardly prove it,


Produce a finite example of what? An equality between 0.9[bar] and 1? What does that mean? I need to find a line with length 1 and a line with length 0.9[bar] and show they're the same length?

That's not how it works. The correct procedure is to define what 0.9[bar] is, then use the definition to show what it is equal to. When you do that as I have done previously in this thread, you see that 0.9[bar] must be equal to 1 and no other number.

or equally important, show the ratio between .999 recurring, and two; is the same as the ratio one to two.


No, once .9[bar] = 1 is proven by limit theory, it follows that all ratios and arithmetic operations you do with 1 can be done with .9[bar] and you will get the same result. The question here is just about the identity itself, not about ratios or sums with other things.

What I said before about the definition of one, means that the identity of anything defined is conserved. A cat is a cat if shaved hairless, or declawed, or neutered. Its definition establishes it as an identity unlike any other. What is the identity of one? It will either be 1, or .999 recurring; and not both, or something else.


A thing has one identity, but it can be uniquely signified in more than one way. The town of Ypsilanti can be uniquely signified as "the town at such-and-such coordinates of latitude and longitude" or as "the first town you approach by walking east from Ann Arbor along Washtenaw Ave". Similarly the number one can be signified as "1", as "the result of the operation 3-2", or "the number approached by the sequence (0.9, 0.99, 0.999...)". The shorthand for that last unique signifier is 0.9[bar].

One can be one, and perhaps .999 recurring can become one; but until it does, it is not one.


Just to be safe I'm going to repeat this again:

0.9[bar] is NOT a sequence or a process or approaching anything. By definition, It is a number approached BY the sequence (.9, .99, .999...). The sequence may be thought of as a process, like a grasshopper jumping from 0.9 to 0.99 to 0.999, etc. But 0.9[bar] is, by definition, the number the grasshopper is getting closer and closer to, not the numbers it is jumping on.
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Re: 1=.999999...?

Postby Juggernaut » Tue Jul 01, 2008 4:56 pm

aporia wrote:
Math may presume such an equality between .999 recurring, and one; but if it cannot produce a finite example of it they can hardly prove it,


Produce a finite example of what? An equality between 0.9[bar] and 1? What does that mean? I need to find a line with length 1 and a line with length 0.9[bar] and show they're the same length?

That's not how it works. The correct procedure is to define what 0.9[bar] is, then use the definition to show what it is equal to. When you do that as I have done previously in this thread, you see that 0.9[bar] must be equal to 1 and no other number.

or equally important, show the ratio between .999 recurring, and two; is the same as the ratio one to two.

Let me say that you are proving my point. Only when one assumes the unit as a arbitrarily arrived one can it even be divided to arrive at .999.... Equalities are never exact. But ones are all around us, even if inexact. Not arbitrary, and not exact, and not equal, except conceptually. And if math did not require the exactness that other models of reality reject, then I would have no problem with what you suggest. There, it is not just one that has to mean something, but equality, and in math, One does not have the meaning of a monad, or of an individual, that is, an undividable unit; because math allows for the infinitely large or small, as reality does not. So, how did you arrive at the length of your line with length, One? Did you use a tape measure with spaces figured in advance? Did you check the temperature, and did you push on the tape, or pull on it.

No, once .9[bar] = 1 is proven by limit theory, it follows that all ratios and arithmetic operations you do with 1 can be done with .9[bar] and you will get the same result. The question here is just about the identity itself, not about ratios or sums with other things.
Nothing is proven by a theory; but it is theories that must be proved, and they never are. Theories are supported by facts, and if you find .9 recurring to be a useful standin, or approximation of One; then use it. Try to be sure that you are not making your math fit your conception of reality.

What I said before about the definition of one, means that the identity of anything defined is conserved. A cat is a cat if shaved hairless, or declawed, or neutered. Its definition establishes it as an identity unlike any other. What is the identity of one? It will either be 1, or .999 recurring; and not both, or something else.


A thing has one identity, but it can be uniquely signified in more than one way. The town of Ypsilanti can be uniquely signified as "the town at such-and-such coordinates of latitude and longitude" or as "the first town you approach by walking east from Ann Arbor along Washtenaw Ave". Similarly the number one can be signified as "1", as "the result of the operation 3-2", or "the number approached by the sequence (0.9, 0.99, 0.999...)". The shorthand for that last unique signifier is 0.9[bar].

One can be one, and perhaps .999 recurring can become one; but until it does, it is not one.

Let me say again, that while one is a symbol, it is also a concept of number. Only one number has to have meaning for all numbers to have meaning, and all the values that all the numbers point to are based upon the value of one, which is natural since that is how we percieve reality as so many units that cannot be properly divided, like people, or planets. If one were purely sign, it would fail if there were two signs for the same reality. It is not reality that makes .9 recurring seem to be a fixed number, but is math taken to an extreme of unreality. It is not really possible to reach 1/3, or 2/3, or any number unless it is changed, and robbed of its meaning. If One is made to be, not a natural unit, but a hundred pounds of rice, arrived at without reference to any naturally occuring One; then you might find 1/3 as a value. By then, the numbers have already been socialized, and taken out of nature, and rely upon and understanding of Pounds as social constructs, etc. Think of it this way: 3-2 is approximately equal to 1. Perhaps .99 recurring is approximately one. But, where we make substitutions there is no point of saying they are equal, because concepts do not work like that. Love is love. There are some close approximations to love, like caring and affection. If the point of our abstractions is understanding then two words for the same value are like two numbers for the same value: confusing and pointless.
Just to be safe I'm going to repeat this again:

0.9[bar] is NOT a sequence or a process or approaching anything. By definition, It is a number approached BY the sequence (.9, .99, .999...). The sequence may be thought of as a process, like a grasshopper jumping from 0.9 to 0.99 to 0.999, etc. But 0.9[bar] is, by definition, the number the grasshopper is getting closer and closer to, not the numbers it is jumping on.
If you want to see .9[Bar] as one, it is not; but it may be that .9[bar] X time, may equal one. The problem is that time changes everything, and by the time .9[bar] equals One today, one will equal something other. Change is the one absolute law of nature. It will make you fat and stupid. Try to get used to it.
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Re: 1=.999999...?

Postby denali » Tue Jul 01, 2008 5:11 pm

juggernaut wrote:Nothing is proven by a theory; but it is theories that must be proved, and they never are. Theories are supported by facts, and if you find .9 recurring to be a useful standin, or approximation of One; then use it. Try to be sure that you are not making your math fit your conception of reality.

You are misunderstanding the term "limit theory." A "theory" in math is just a body of mathematical definitions and theorems that are grouped together. There are no facts because numbers are defined a priori.
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Re: 1=.999999...?

Postby aporia » Tue Jul 01, 2008 6:23 pm

Let me say again, that while one is a symbol, it is also a concept of number.


I have no idea what this means. Suppose I said "duck is a symbol, but it is also a concept of duck". Do you have any idea what that means? At the very least that sentence is highly confusing.

The problem is you're conflating signifier and signified. There is an easy way to distinguish them. If I want to talk about a specific duck or the concept of duck, I say duck. If I want to talk about the signifier word which means duck, I put it in quotation marks: "duck". Duck is an animal signified by the word "duck". They are distinct; one is an animal and one is a word. Why would this change in the case of one and "one"?

3-2 is approximately equal to 1.


What in the world? If 3-2 is not exactly equal to 1, what is the difference between 3-2 and 1?
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Re: 1=.999999...?

Postby Juggernaut » Wed Jul 02, 2008 3:20 am

denali wrote:
juggernaut wrote:Nothing is proven by a theory; but it is theories that must be proved, and they never are. Theories are supported by facts, and if you find .9 recurring to be a useful standin, or approximation of One; then use it. Try to be sure that you are not making your math fit your conception of reality.

You are misunderstanding the term "limit theory." A "theory" in math is just a body of mathematical definitions and theorems that are grouped together. There are no facts because numbers are defined a priori.

What makes you say numbers are defined a priori? One number has a natural definition, and that is one, because we can count the entire contents of the cosmos with ones. All other numbers are in some ratio to one. Now, however one is defined, it must still be proved, and we are about that now. And in this regard, one is no different than any other concept because if the concept were of a rose, every rose would either prove the concept absolute (to a greater degree of certainty), -and identity true; or shows them to be wrong. That is: if you should find a rose that fits the definition of a rose in every detail save one, either the definition is wrong, or the rose in question needs its own classification. If the definition, and the identity of one is 1., it cannot, for mere convenience be otherwise. Further more, Math is an abstraction of reality, and math cannot be used to prove math, so reality must prove math. What is the reality that proves the concept of .9 [bar] is the equal of the concept One? For example: The abstraction of the reality 'rose', cannot be used to prove the rose real, but the reality 'rose', can be used to prove the definition and identity a abstraction of rose (though never absolutly). Does that make sense to you, that we do not test reality but use reality to test concepts?
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Re: 1=.999999...?

Postby Juggernaut » Wed Jul 02, 2008 3:48 am

aporia wrote:
Let me say again, that while one is a symbol, it is also a concept of number.


I have no idea what this means. Suppose I said "duck is a symbol, but it is also a concept of duck". Do you have any idea what that means? At the very least that sentence is highly confusing.

The problem is you're conflating signifier and signified. There is an easy way to distinguish them. If I want to talk about a specific duck or the concept of duck, I say duck. If I want to talk about the signifier word which means duck, I put it in quotation marks: "duck". Duck is an animal signified by the word "duck". They are distinct; one is an animal and one is a word. Why would this change in the case of one and "one"?

3-2 is approximately equal to 1.


What in the world? If 3-2 is not exactly equal to 1, what is the difference between 3-2 and 1?

In math only one, as a number has meaning, and there is only one 'number' necessary in concept. Since all other numbers get their meaning based upon one, they are signs, and one is the concept. Now; there are sets of numbers that are conceptual manifolds in themselves; but no less than others, their meaning rests on one. Think of how primitives may have counted before the concept of number. We have our natural five, and I have seen some primitives count ten on their wrists, and twenty on their elbow. Inevitably one begins with one, and so the unit, and the monad, is both concept and sign. In one of these dictionaries around here Idea was in part defined as: one thing. If this is so then the conceptual duck is a single duck having the qualities of all ducks. And the word 'Duck' can also be a sign pointing to any duck. Now, there are many phenomena that seem to have meaning even though as infinites they cannot be concieved of. We all sort of give a subjective value to existence, or the cosmos, or to God; but we cannot measure the meaning against the reality. With finite reality we stand on firmer ground, and I think it is for that reason, in part, that people sometimes thought the concept preceeded the reality. It is because every concept represents a measure of perfection that reality does not. Every conceptual one is equal, and no real one is equal. Men are all the equal of men, but it is the concept 'man' which makes them so. Since concepts are both abstractions, and general, they can be perfect; but reality is what it is. In saying 3-2 approximates 1, it is because only in math does one equal one. It is not something that can be demonstrated. Rather you need the insight to realize how futile is math at giving an exact picture of reality. The uncertanty principal is one aspect of it, but the fact remains that we cannot at the same instant measure reality and measure our measurments. And still math is correct, because it is generally correct, and can be corrected as it goes along.
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Re: 1=.999999...?

Postby Kermit1941 » Sun Aug 03, 2008 2:03 am

Why do we make the convention that

.9999999999999999999999. . . = 1?


Because .999999999999999999.... does not look like

1.000000000000000000000000000.....

Some people feel intuitively that they cannot be the same real number.

The fact is that real numbers have been defined in such a way that if the difference of two real numbers
are an infinitesimal, then those two real numbers are considered to be equal.

It is because the difference of 1.00000000000000000000000...

and .9999999999999999999999999...

is an infinitesimal, that we say that


1.0000000000000000000000000..... and .999999999999999999999999....

are equal.


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Re: 1=.999999...?

Postby Juggernaut » Sun Aug 03, 2008 3:26 am

Kermit1941 wrote:Why do we make the convention that

.9999999999999999999999. . . = 1?


Because .999999999999999999.... does not look like

1.000000000000000000000000000.....

Some people feel intuitively that they cannot be the same real number.

The fact is that real numbers have been defined in such a way that if the difference of two real numbers
are an infinitesimal, then those two real numbers are considered to be equal.

It is because the difference of 1.00000000000000000000000...

and .9999999999999999999999999...

is an infinitesimal, that we say that


1.0000000000000000000000000..... and .999999999999999999999999....

are equal.


Kermit Rose

That would be just fine. It is certainly close enough for the girls I go with, because if they could see straight they wouldn't go out with me. The problem is that we take identity to be the same as equality, and it is not always so. The father is the same as the son plus time, and time changes everything. But today, at a fixed point in time, .999... does not equal one, and it is not identical to one. And the identity is most important since for symbols to work they must be identified, and identifiable. And of all numbers, one is not just symbol, and identity, but also is concept; the single concept essential to math. So, if you are doing anything practical in nature, .99 is equal to 1. With the concept of one, perfection is not required because no one is the equal of another. Math is another story, and it cannot have some other number both equal to one and not equal to one. Since, if it were equal to one, it would be one, it can safely be said that .999... is not equal to one, because one is fixed in time, and is a measure of reality, as no infinitely recuring series can be. What do you think
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Re: 1=.999999...?

Postby Wonderer » Sun Aug 03, 2008 10:23 pm

Kermit1941 wrote:Why do we make the convention that

.9999999999999999999999. . . = 1?


Because .999999999999999999.... does not look like

1.000000000000000000000000000.....

Some people feel intuitively that they cannot be the same real number.

The fact is that real numbers have been defined in such a way that if the difference of two real numbers
are an infinitesimal, then those two real numbers are considered to be equal.

It is because the difference of 1.00000000000000000000000...

and .9999999999999999999999999...

is an infinitesimal, that we say that


1.0000000000000000000000000..... and .999999999999999999999999....

are equal.


Kermit Rose


The thing is, infintesimals aren't zero by definition.

This slack attempt at a rationalisation of the problem defined in this thread is somewhat lacking.

.333[bar] doesn't equal 1/3 in my opinion.

.999[bar] is an impossible ideal to which we give an impossible answer.

It doesn't exist outside of the non material world inside your head.

The math that we all know and love which deals with real quantities had no part in the incestuous conception of what has become blind faith in a logically flawed ideal.

sure you can use .333[bar] as equal to 1/3 and .999[bar] as equal to 1, but you're not doing math so much as your're doing dictation.
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Re: 1=.999999...?

Postby Juggernaut » Sun Aug 03, 2008 10:34 pm

I don't think math deals with real quantities, excepting the essential quantity to math, of one. And 1/3, and .333... are not numbers exactly, but ratios. When seeing 1/3, what must be know for the number to have significance is one. If it is a pound, a mile, or a bag of sugar, then the 1/3 has some meaning. Apart, as part of a system of abstraction, 1/3 is not an answer, but is a question phrased as an answer.
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Re: 1=.999999...?

Postby Wonderer » Sun Aug 03, 2008 10:39 pm

Juggernaut wrote:I don't think math deals with real quantities, excepting the essential quantity to math, of one. And 1/3, and .333... are not numbers exactly, but ratios. When seeing 1/3, what must be know for the number to have significance is one. If it is a pound, a mile, or a bag of sugar, then the 1/3 has some meaning. Apart, as part of a system of abstraction, 1/3 is not an answer, but is a question phrased as an answer.


i'm talking about 1 orange, 2 oranges 1 and a half oranges. thse are real numbers.

i also think that 1 third orange is a real quantity.

our number system simply prevents us from writing it out in digit form.

the amount confusions that result from this simple fact are incredible.
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