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Post by general313 on May 10, 2020 16:19:08 GMT
It doesn't matter whether they studied calculus, and I very much doubt that anyone can find a mathematician who hasn't. Since you mentioned the decimal representation of 1/7, it should be pointed out that that representation is exact. Hence one can use the equation 1/7 = 0.142857142857... One does not need to use the approximately equal symbol here (≈). First of all no, many decimal representations are not exact, including that of 1/7. Secondly. even if they were exact, no one has that many digits. Most Calculators do not store more than 15 digits, less expensive ones only 8 digits. Microsoft Excel only uses as many as 15 digits. I wrote a program that can do 100 digit calculations, but I knew full well at the time it is only good for philosophical investigations into the properties of numbers. There is no real world measurement that precise. You are talking about even larger numbers of digits. No matter how small you write you can't get that many digits on a ream of paper. Even Watson the supercomputer can't work with that many digits. It then becomes irrelevant what that many digits might "equal," does it not? In any actual use of mathematics for real world computations it is not a matter of exactitude, it is a matter of necessary precision, for example ±10 -8 is beyond anything you will likely need. You may of course use any notation you wish as long as you and your associates understand each other. It is exact. If is not, then tell me how much in error the infinite sum is from the fraction. Mathematicians do have that many digits; calculator precision is beside the point.
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Post by Arlon10 on May 10, 2020 20:33:24 GMT
First of all no, many decimal representations are not exact, including that of 1/7. Secondly. even if they were exact, no one has that many digits. Most Calculators do not store more than 15 digits, less expensive ones only 8 digits. Microsoft Excel only uses as many as 15 digits. I wrote a program that can do 100 digit calculations, but I knew full well at the time it is only good for philosophical investigations into the properties of numbers. There is no real world measurement that precise. You are talking about even larger numbers of digits. No matter how small you write you can't get that many digits on a ream of paper. Even Watson the supercomputer can't work with that many digits. It then becomes irrelevant what that many digits might "equal," does it not? In any actual use of mathematics for real world computations it is not a matter of exactitude, it is a matter of necessary precision, for example ±10 -8 is beyond anything you will likely need. You may of course use any notation you wish as long as you and your associates understand each other. It is exact. If is not, then tell me how much in error the infinite sum is from the fraction. Mathematicians do have that many digits; calculator precision is beside the point. The difference is described as "infinitesimal" which must be larger than zero because there must always be ("infinite" process, remember) an even smaller number before reaching zero. In order for the sum to be equal to 1 the difference must actually be zero which it never is. While indeed the difference is negligible in all real world applications that does not mean there is an actual equality. No, mathematicians do not confuse any ongoing process with fixed quantities, just retarded atheists who think they are mathematicians or scientists simply because they failed religion too. If "infinitesimal" means the "same" thing as "zero" why not just say zero?
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Post by general313 on May 10, 2020 21:05:40 GMT
It is exact. If is not, then tell me how much in error the infinite sum is from the fraction. Mathematicians do have that many digits; calculator precision is beside the point. The difference is described as "infinitesimal" which must be larger than zero because there must always be ("infinite" process, remember) an even smaller number before reaching zero. In order for the sum to be equal to 1 the difference must actually be zero which it never is. While indeed the difference is negligible in all real world applications that does not mean there is an actual equality. No, mathematicians do not confuse any ongoing process with fixed quantities, just retarded atheists who think they are mathematicians or scientists simply because they failed religion too. If "infinitesimal" means the "same" thing as "zero" why not just say zero? You are quite wrong. The decimal expansion of a number such as 1/7 is by definition the exact representation of that number. In other words, (1/7) - (0.142857142857...) = 0. You seem to be suffering from the misconception that since there's an infinity of numbers that the task of summing can never be completed. This is wrong, as can be demonstrated, going back to one of the examples from Zeno's paradoxes: divide a one-meter bar into the first half, the remaining half in two, ad infinitum. There are an infinite number of such half segments. Now, how long will it take to traverse all of these half segments when travelling at 1 meter per second? The answer is one second. We crossed an infinite number of segments in finite time. Nothing special about this really, we're essentially chopping up a finite time the same way we're chopping up a finite distance. By the way, if you're going to continue using misplaced childish insults, I may just tell you to go fuck yourself.
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Post by Arlon10 on May 10, 2020 21:57:51 GMT
The difference is described as "infinitesimal" which must be larger than zero because there must always be ("infinite" process, remember) an even smaller number before reaching zero. In order for the sum to be equal to 1 the difference must actually be zero which it never is. While indeed the difference is negligible in all real world applications that does not mean there is an actual equality. No, mathematicians do not confuse any ongoing process with fixed quantities, just retarded atheists who think they are mathematicians or scientists simply because they failed religion too. If "infinitesimal" means the "same" thing as "zero" why not just say zero? You are quite wrong. The decimal expansion of a number such as 1/7 is by definition the exact representation of that number. In other words, (1/7) - (0.142857142857...) = 0. You seem to be suffering from the misconception that since there's an infinity of numbers that the task of summing can never be completed. This is wrong, as can be demonstrated, going back to one of the examples from Zeno's paradoxes: divide a one-meter bar into the first half, the remaining half in two, ad infinitum. There are an infinite number of such half segments. Now, how long will it take to traverse all of these half segments when travelling at 1 meter per second? The answer is one second. We crossed an infinite number of segments in finite time. Nothing special about this really, we're essentially chopping up a finite time the same way we're chopping up a finite distance. By the way, if you're going to continue using misplaced childish insults, I may just tell you to go fuck yourself. You seem to believe that it makes any difference what you call anything. It does make a difference, but only to you and your associates. You are not in charge here for example. I'm sure you can sell all sorts of cheap calculators with your attitude. I have one that uses better forms of expression rather easily. It has been thoroughly explained to you that the decimal representation of 1/7 is an ongoing process, and how that is different from a quantity. I have allowed you your right to arbitrarily define it however your work group finds it convenient. You do need to go, not I. My terminology "limit" is recognized by enough professionals that we can be fine without your contributions. You asked what the difference between 1 and an infinite string of 9s after a decimal point is and I explained it. Another way to explain it is 1/∞. However that is algebraic manipulation of something which is not a quantity, which is not allowed. Infinity is not a quantity. Is Infinity or 3 times infinity larger? There is no good answer. If infinity or infinity minus a million larger? There is no good answer. Why is that? That is because infinity is not a quantity, it is a continuing process, "3" and a "million" are fixed quantities. A topic for recreational speculation is whether there can be manipulation of processes where no fixed quantities are involved such as is infinity minus infinity zero? Play with that all day if you wish.
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Post by general313 on May 10, 2020 22:24:35 GMT
You are quite wrong. The decimal expansion of a number such as 1/7 is by definition the exact representation of that number. In other words, (1/7) - (0.142857142857...) = 0. You seem to be suffering from the misconception that since there's an infinity of numbers that the task of summing can never be completed. This is wrong, as can be demonstrated, going back to one of the examples from Zeno's paradoxes: divide a one-meter bar into the first half, the remaining half in two, ad infinitum. There are an infinite number of such half segments. Now, how long will it take to traverse all of these half segments when travelling at 1 meter per second? The answer is one second. We crossed an infinite number of segments in finite time. Nothing special about this really, we're essentially chopping up a finite time the same way we're chopping up a finite distance. By the way, if you're going to continue using misplaced childish insults, I may just tell you to go fuck yourself. You seem to believe that it makes any difference what you call anything. It does make a difference, but only to you and your associates. You are not in charge here for example. I'm sure you can sell all sorts of cheap calculators with your attitude. I have one that uses better forms of expression rather easily. It has been thoroughly explained to you that the decimal representation of 1/7 is an ongoing process, and how that is different from a quantity. I have allowed you your right to arbitrarily define it however your work group finds it convenient. You do need to go, not I. My terminology "limit" is recognized by enough professionals that we can be fine without your contributions. You asked what the difference between 1 and an infinite string of 9s after a decimal point is and I explained it. Another way to explain it is 1/∞. However that is algebraic manipulation of something which is not a quantity, which is not allowed. Infinity is not a quantity. Is Infinity or 3 times infinity larger? There is no good answer. If infinity or infinity minus a million larger? There is no good answer. Why is that? That is because infinity is not a quantity, it is a continuing process, "3" and a "million" are fixed quantities. A topic for recreational speculation is whether there can be manipulation of processes where no fixed quantities are involved such as is infinity minus infinity zero? Play with that all day if you wish. As usual, you have avoided the point in my second paragraph. So I ask the question: if one subdivides a one meter length into a first half (length 1/2), a first remaining quarter, a first remaining eighth, a first remaining 1/16th, ad infinitum, how many segments are there?
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Post by Arlon10 on May 10, 2020 22:49:11 GMT
You seem to believe that it makes any difference what you call anything. It does make a difference, but only to you and your associates. You are not in charge here for example. I'm sure you can sell all sorts of cheap calculators with your attitude. I have one that uses better forms of expression rather easily. It has been thoroughly explained to you that the decimal representation of 1/7 is an ongoing process, and how that is different from a quantity. I have allowed you your right to arbitrarily define it however your work group finds it convenient. You do need to go, not I. My terminology "limit" is recognized by enough professionals that we can be fine without your contributions. You asked what the difference between 1 and an infinite string of 9s after a decimal point is and I explained it. Another way to explain it is 1/∞. However that is algebraic manipulation of something which is not a quantity, which is not allowed. Infinity is not a quantity. Is Infinity or 3 times infinity larger? There is no good answer. If infinity or infinity minus a million larger? There is no good answer. Why is that? That is because infinity is not a quantity, it is a continuing process, "3" and a "million" are fixed quantities. A topic for recreational speculation is whether there can be manipulation of processes where no fixed quantities are involved such as is infinity minus infinity zero? Play with that all day if you wish. As usual, you have avoided the point in my second paragraph. So I ask the question: if one subdivides a one meter length into a first half (length 1/2), a first remaining quarter, a first remaining eighth, a first remaining 1/16th, ad infinitum, how many segments are there? A one meter length of what? Obviously matter has a point beyond which you will need to split protons and that could have unpredictable results. If you mean a theoretical meter, that could go on forever.
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Post by general313 on May 10, 2020 23:27:41 GMT
As usual, you have avoided the point in my second paragraph. So I ask the question: if one subdivides a one meter length into a first half (length 1/2), a first remaining quarter, a first remaining eighth, a first remaining 1/16th, ad infinitum, how many segments are there? A one meter length of what? Obviously matter has a point beyond which you will need to split protons and that could have unpredictable results. If you mean a theoretical meter, that could go on forever. You can use empty space or the same material that Zeno had in mind.
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Post by Arlon10 on May 10, 2020 23:50:10 GMT
A one meter length of what? Obviously matter has a point beyond which you will need to split protons and that could have unpredictable results. If you mean a theoretical meter, that could go on forever. You can use empty space or the same material that Zeno had in mind. Has this any point? If so what? If your point is that that the halving "approaches" a meter, I've already explained that is the terminology used in calculus, "limits" are "approached."
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Post by general313 on May 11, 2020 17:03:46 GMT
You can use empty space or the same material that Zeno had in mind. Has this any point? If so what? If your point is that that the halving "approaches" a meter, I've already explained that is the terminology used in calculus, "limits" are "approached." It's your thread, you tell me. Just answer the question, it should just take a few seconds of thought, even for you.
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