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.
Moderator: Flannel Jesus
Aidan_Mclaren wrote:Do you really see fruit being bared, or do you pretend to see it?
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.
Aidan_Mclaren wrote:I thought we already did.
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.
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.
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
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 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?
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.
Which physics problems that you know of depending upon an infinite series for their solution
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?
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?
Aidan_Mclaren wrote:So by that, you admit "0.999 recurring equals 1" is a logical shortcut?
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.
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.
One can be one, and perhaps .999 recurring can become one; but until it does, it is not one.
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.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.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.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.
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.
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.
Let me say again, that while one is a symbol, it is also a concept of number.
3-2 is approximately equal to 1.
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.
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?
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
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
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.
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