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Warn moderators| Author : | Topic: mathematics | Bottom |
| saucer admin Posts : 673 A Good Tautology is Hard to Find!  |
- FACTORIALS I need the factorial value for 83,000 (eighty three thousand) or 83000(!). That is 83000 x 82999 x 82998 x 82997 etc. I prefer answer in the form N.nnn times 10 to the eXponent. If you use a stat program, I need the name of the Stat program used. --- 83000! = 7.91222558e372239 Note: because you wanted it in exponential notation it is an approximate value, the actual value would take a few thousand lines in this message box, but I can post it if you want it, or you can do it yourself with the instructions below. To figure this out, I used an infinite precision math package written for the Tcl scrïpting language called Mpexpr. I had this already installed on my computer so I just wrote a small program that computed this value, here is the program: package require Mpexpr set factorial [mpformat "%e" [mpexpr fact(83000)]] And that is all there is to it (I say that as if it were nothing, but in fact it took almost 30 minutes to compute the factorial and format it on my computer). To run the factorial, assuming you have Tcl and Mpexpr installed on your system (if you don't have them, I have included instructions below), you would execute the main tcl (tclsh) executable. It will give you a prompt that looks like this: % then you just type in those 2 lines above, and it computes the factorial for you, and formats it in exponential notation. If you don't have Tcl and Mpexpr installed on your system then you can download them and install them from the following websites, they are both freely available: To get Tcl installed you should goto the Tcl website: "Tcl 8.0" http://www.scrïptics.com/software/tcltk/8.0.html#Download Binary Simply download the Windows Tcl self-extracting installer, and run the tcl805.exe file. That should install Tcl. To get the Mpexpr package installed do the following: "Mpexpr download" http://www.NeoSoft.com/tcl/ftparchive/sorted/math/Mpexpr-1.0/1.0/mpexpr-1.0.tar.gz The once you download the Mpexpr package you can unzip it using any zip utility (WinZip, PkZip, etc...) and then you should goto the mpexpr-1.0\win directory, and read the README.win file, it will tell you how to complete the install. Courtesy: http://answers.google.com/answers/threadview?id=33709 - --Last edited by saucer on 2007-06-01 08:36:23 -- |
| experi-momentum Posts : 13  |
Zero is "not there" Judging from the treatment accorded to the concept of zero, we do practice a variety of avoidance mechanisms rather than confront the imagery associated with this seemingly difficult concept. In reciting one's telephone number, social security number, postal zip code or post office box, room number, street number or any of a variety of other numeric nominals, we carefully avoid pronouncing the digit "zero" and instead substitute "oh." One may say "it is caused by our desire to communicate quickly, if we can say the same thing in one syllable, why not?" What about number seven, should we find a substitute for this too? In some parts of the world, the phrasing "naught" and "aught" are used but it is quite uncommon to hear "zero." All the other digits are correctly enunciated with this one curious exception. However, in the US Army there is an additional curious habit of saying "duece" instead of "two". For example, the M102 105mm Artillery Cannon is called a "One oh Duece" (notice the "oh" therein). Is the presence of nothing (reflecting non-existence) different from the absence of something (reflecting non-availability) or the absence of anything (reflecting non-existence)? Zero is a symbol for "not there" which is different from "nothing" "Not there" reflects that the number or item(s) exists but they are not just available. "Nothing" reflects nonexistence. There is also "the Zero Factor about the US Presidents" known as the Zero Factor and Tecumseh's Curse which is the curse of Indian chief Tecumseh which has Killed every U.S. President before the end of their term in office, if they were elected in a year that ended with 0. The first victim of the curse was William Henry Harrison, whose troops killed the Indian chief in 1813 (the zero factor has one exception, i.e., Ronald Reagan who was elected in 1980). Zero not only has the quality of being nothing, it is also a noun, verb, adverb, and an adjective as in "zero possibility". "We zeroed in on the cause," means we had isolated all the possibilities, and have discovered the one remaining. In this use as a verb, zero equals one. However, "The result was a big, fat, zero," uses the noun to express the idea of results of "nothing". Here, zero has the quality of not being there. Zero as an action appears in the Conservative Laws of physics. The term "zeroing in on (whatever)" might have originated also with the military. The "zero" in this term might refer to the distance from the last bomb dropped or the last shell fired to some target. The aim is always to try in reducing this distance to zero. On a roulette wheel, there is the number Zero which is neither Red nor Black. Zero is the GREEN number, for all the cash the house rakes in when it comes up. It is considered neither Even nor Odd. Is zero a number? Consider the following scene: Ernie: I've put a number of cookies in that Jar. You can have them if you give me your teddy. Bert: Great While Ernie hands over the teddy and looks eagerly in the jar, said: Bert "Wait a Minute There's No Cookies Here. You Said You Put a Number of Cookies in There" Ernie: That's right, zero is a number. It is not uncommon these days to hear, on dating scene, the phrase "get rid of the 'zero' and get yourself a hero". Zero is often used in the descrïption of an undesirable individual as illustrated in following cartoon: Click on the image to enlarge. A Sociological Application of Zero Clearly some sort of an avoidance mechanism is in operation. It is as though the name itself invokes a kind of anxiety perhaps associated with "nothingness", a kind of emptiness which humankind finds uncomfortable and prefer to avoid confronting. As with all such anxiety- provoking ideas, some other imagery is substituted which provides a veneer to mask the disquieting emotional undertones of the discomforting idea. Zero represents the amount of nothing. Today zero has a meaning not just of a number, but as the bottom, or failure. He made no baskets, or, he made zero baskets -- meaning he failed to score. Or he gave zero assistance. If you are familiar with numerology, you notice that there is no zero to work with in the numbers that correlate with the alphabet, strange? Not at all. The absence of zero may suggest that the Pythagorean who first developed the duality between numbers and letters were not aware of the zero notion. The notion of zero is much younger. In tennis scores, zero is called "love," because zero looks like an egg, the French called it "l'oeuf," which is French for "egg." You may have also noticed the weird numbering in the tennis scores which goes back to medieval numerology, in which 60 was considered a "complete" number (much like 100 is considered a nice round number today). Back in medieval times, tennis's four points were 15, 30, 45 (later abbreviated to 40), and 60, or game. On the telephone keypad, zero has the honor of representing the operator. There is no zero in most games, such as plying cards (after all who wants to win zero!). Zero is placed at the end of the keypad on the computer and at the bottom of the keypad on the telephone. Is zero the beginning or the end? Notice that on a calculator's keypad the numbers starts with the largest numbers on the top and work their way down to zero. What about the o and 0 being right next to each other on the PC keyboard? Numbers are located three places. First it is located on the keyboard keys with the range 1, 2,...,0; this is the same order that phone keypad. Second, on the right of the keyboard is a calculator-like pad where zero is the last listed number. Finally, there is a list of functions key, however there is no F0 because that could translate into no function and what would be the point of having a key "without" function. There will always be questions about the true meaning and function of zero. Is it the end or the beginning? What does ground zero mean? Some use it as starting point; the military uses it as an ending point. The resistance against zero can be noted even at the architectural level in buildings where the ground-level is rarely denoted as the zeroth-level as it should be. However, for mathematicians it comes easily to label the floors of a building to include zero, for example, the Department of Mathematics' building at the University of Zagreb in Croatia has floors numbered as -1, 0, 1, 2, and 3. In fact, this is not a particularity of one building but a common practice in modern buildings in large cities such as Buenos Aires. In most European countries the floors are always numbered starting from 0. We do have a special word to say 'ground floor' in a conversation, not using 0, but the elevators will always offer you a "0 button" for the ground floor. Now is the time to test yourself. Consider 0/0 (zero divided by zero) which of the following takes precedence and why? A: Any number divided by zero is meaningless; B: Zero divided by any number is zero; C: Any number divided by itself is 1. By now you should know the answer and the why. For example, for Part C: Any number divided by itself is 1.", which is a true statement for zero. That is 0/0 is also meaningless. One may still argue that 0/0 = 1. Well, if we allow this you end up with some inconsistent results. For example, you end up showing 5 = 1: 5 = 5 . (1) = 5 . (0/0) = [5 . (0)] / 0 = 0/0 = 1 One may say that "I understand why it's considered meaningless to divide a number by 0. But why is the answer considered meaningless when dividing 0 by 0? I think of it as 0 / 0 = x. Zero times x = 0. This is possible because anything multiplied by zero equals zero." The problem with this argument is that "What is the value of x?" It could be any number therefore, one number cannot be equal to so many different numbers. Thus, 0/0 is indeed meaningless. Therefore, teaching our young students that "0/0 = Any Number (AN); this is equivalent to AN x 0 = 0." is wrong. One should never divide by zero. Division by zero is a meaningless operation. How could you divide 3 apples among zero people! How could you divide "nothing" among nobody! You may like to visit and find out what is wrong in the following Web site: Paul, a 3rd grader, divides by ZERO. One of my readers wrote to me that: ".... what is 0/0? This is equal to any number because when you multiply any number by zero, you get zero. This is why 0/0 is an indeterminate quantity. Is it correct to say x/y = z/y implies x = z unless y = 0? The main problem I have with this line of argument is "the act of dividing by zero" which is meaningless Therefore, it does not make to ask further what is its result, whether it is indeterminate or not. |
| experi-momentum Posts : 13 |
Zero is "not there" Judging from the treatment accorded to the concept of zero, we do practice a variety of avoidance mechanisms rather than confront the imagery associated with this seemingly difficult concept. In reciting one's telephone number, social security number, postal zip code or post office box, room number, street number or any of a variety of other numeric nominals, we carefully avoid pronouncing the digit "zero" and instead substitute "oh." One may say "it is caused by our desire to communicate quickly, if we can say the same thing in one syllable, why not?" What about number seven, should we find a substitute for this too? In some parts of the world, the phrasing "naught" and "aught" are used but it is quite uncommon to hear "zero." All the other digits are correctly enunciated with this one curious exception. However, in the US Army there is an additional curious habit of saying "duece" instead of "two". For example, the M102 105mm Artillery Cannon is called a "One oh Duece" (notice the "oh" therein). Is the presence of nothing (reflecting non-existence) different from the absence of something (reflecting non-availability) or the absence of anything (reflecting non-existence)? Zero is a symbol for "not there" which is different from "nothing" "Not there" reflects that the number or item(s) exists but they are not just available. "Nothing" reflects nonexistence. There is also "the Zero Factor about the US Presidents" known as the Zero Factor and Tecumseh's Curse which is the curse of Indian chief Tecumseh which has Killed every U.S. President before the end of their term in office, if they were elected in a year that ended with 0. The first victim of the curse was William Henry Harrison, whose troops killed the Indian chief in 1813 (the zero factor has one exception, i.e., Ronald Reagan who was elected in 1980). Zero not only has the quality of being nothing, it is also a noun, verb, adverb, and an adjective as in "zero possibility". "We zeroed in on the cause," means we had isolated all the possibilities, and have discovered the one remaining. In this use as a verb, zero equals one. However, "The result was a big, fat, zero," uses the noun to express the idea of results of "nothing". Here, zero has the quality of not being there. Zero as an action appears in the Conservative Laws of physics. The term "zeroing in on (whatever)" might have originated also with the military. The "zero" in this term might refer to the distance from the last bomb dropped or the last shell fired to some target. The aim is always to try in reducing this distance to zero. On a roulette wheel, there is the number Zero which is neither Red nor Black. Zero is the GREEN number, for all the cash the house rakes in when it comes up. It is considered neither Even nor Odd. Is zero a number? Consider the following scene: Ernie: I've put a number of cookies in that Jar. You can have them if you give me your teddy. Bert: Great While Ernie hands over the teddy and looks eagerly in the jar, said: Bert "Wait a Minute There's No Cookies Here. You Said You Put a Number of Cookies in There" Ernie: That's right, zero is a number. It is not uncommon these days to hear, on dating scene, the phrase "get rid of the 'zero' and get yourself a hero". Zero is often used in the descrïption of an undesirable individual as illustrated in following cartoon: A Sociological Application of Zero Clearly some sort of an avoidance mechanism is in operation. It is as though the name itself invokes a kind of anxiety perhaps associated with "nothingness", a kind of emptiness which humankind finds uncomfortable and prefer to avoid confronting. As with all such anxiety- provoking ideas, some other imagery is substituted which provides a veneer to mask the disquieting emotional undertones of the discomforting idea. Zero represents the amount of nothing. Today zero has a meaning not just of a number, but as the bottom, or failure. He made no baskets, or, he made zero baskets -- meaning he failed to score. Or he gave zero assistance. If you are familiar with numerology, you notice that there is no zero to work with in the numbers that correlate with the alphabet, strange? Not at all. The absence of zero may suggest that the Pythagorean who first developed the duality between numbers and letters were not aware of the zero notion. The notion of zero is much younger. In tennis scores, zero is called "love," because zero looks like an egg, the French called it "l'oeuf," which is French for "egg." You may have also noticed the weird numbering in the tennis scores which goes back to medieval numerology, in which 60 was considered a "complete" number (much like 100 is considered a nice round number today). Back in medieval times, tennis's four points were 15, 30, 45 (later abbreviated to 40), and 60, or game. On the telephone keypad, zero has the honor of representing the operator. There is no zero in most games, such as plying cards (after all who wants to win zero!). Zero is placed at the end of the keypad on the computer and at the bottom of the keypad on the telephone. Is zero the beginning or the end? Notice that on a calculator's keypad the numbers starts with the largest numbers on the top and work their way down to zero. What about the o and 0 being right next to each other on the PC keyboard? Numbers are located three places. First it is located on the keyboard keys with the range 1, 2,...,0; this is the same order that phone keypad. Second, on the right of the keyboard is a calculator-like pad where zero is the last listed number. Finally, there is a list of functions key, however there is no F0 because that could translate into no function and what would be the point of having a key "without" function. There will always be questions about the true meaning and function of zero. Is it the end or the beginning? What does ground zero mean? Some use it as starting point; the military uses it as an ending point. The resistance against zero can be noted even at the architectural level in buildings where the ground-level is rarely denoted as the zeroth-level as it should be. However, for mathematicians it comes easily to label the floors of a building to include zero, for example, the Department of Mathematics' building at the University of Zagreb in Croatia has floors numbered as -1, 0, 1, 2, and 3. In fact, this is not a particularity of one building but a common practice in modern buildings in large cities such as Buenos Aires. In most European countries the floors are always numbered starting from 0. We do have a special word to say 'ground floor' in a conversation, not using 0, but the elevators will always offer you a "0 button" for the ground floor. Now is the time to test yourself. Consider 0/0 (zero divided by zero) which of the following takes precedence and why? A: Any number divided by zero is meaningless; B: Zero divided by any number is zero; C: Any number divided by itself is 1. By now you should know the answer and the why. For example, for Part C: Any number divided by itself is 1.", which is a true statement for zero. That is 0/0 is also meaningless. One may still argue that 0/0 = 1. Well, if we allow this you end up with some inconsistent results. For example, you end up showing 5 = 1: 5 = 5 . (1) = 5 . (0/0) = [5 . (0)] / 0 = 0/0 = 1 One may say that "I understand why it's considered meaningless to divide a number by 0. But why is the answer considered meaningless when dividing 0 by 0? I think of it as 0 / 0 = x. Zero times x = 0. This is possible because anything multiplied by zero equals zero." The problem with this argument is that "What is the value of x?" It could be any number therefore, one number cannot be equal to so many different numbers. Thus, 0/0 is indeed meaningless. Therefore, teaching our young students that "0/0 = Any Number (AN); this is equivalent to AN x 0 = 0." is wrong. One should never divide by zero. Division by zero is a meaningless operation. How could you divide 3 apples among zero people! How could you divide "nothing" among nobody! You may like to visit and find out what is wrong in the following Web site: Paul, a 3rd grader, divides by ZERO. One of my readers wrote to me that: ".... what is 0/0? This is equal to any number because when you multiply any number by zero, you get zero. This is why 0/0 is an indeterminate quantity. Is it correct to say x/y = z/y implies x = z unless y = 0? The main problem I have with this line of argument is "the act of dividing by zero" which is meaningless Therefore, it does not make to ask further what is its result, whether it is indeterminate or not. courtesy: http://home.ubalt.edu/ntsbarsh/zero/ZERO.HTM#rzeronot experi-momentum --Last edited by experi-momentum on 2007-08-27 00:37:11 -- |
| saucer admin Posts : 673 A Good Tautology is Hard to Find! |
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| saucer admin Posts : 673 A Good Tautology is Hard to Find! |
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