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Posted: 6/19/2002 2:48:08 PM EDT
[Last Edit: 6/19/2002 3:46:49 PM EDT by The_Macallan]
...that you only found out was wrong many years later? The recent algebra thread by [b]Sweep[/b] made me think back to school at some of the major errors that teachers taught to me that only years later I learned were not true. Mine was also a math-related lesson: One of my math teachers in school taught me that when rounding decimals, that x.1, x.2, x.3, x.4 all round down to x while x.6., x.7, x.8 and x.9 all round up to y. No problem there. THIS is what I was taught to do with "x.5" * If x is an even number, round x.5 down, * If y is an even number, round x.5 up. In other words, always round x.5 to the largest EVEN NUMBER! 3.5 rounds to 4 4.5 rounds to 4 5.5 rounds to 6 UGH!!! That stupidity stayed with me for YEARS!! If I ever see Mr. Charzen again, I'll be sure to smack him 39.5 times! [BD] What stupidity were you taught in school that years later you found out was really wrong. [b]Please - no lessons on evolution or creationism or religion etc.!![/b] edited for clarity.
Link Posted: 6/19/2002 2:53:14 PM EDT
What about my highschool history teacher trying to tell me that the Civil War was only fought to free the slaves? I knew better even back then.
Link Posted: 6/19/2002 3:02:53 PM EDT
The Nuns at Saint Joes told me that missing church on sunday was a mortal sin and I would go to hell.. Havent been to church in 20 years... Guess I'm Hell bent... [Rolleyes]
Link Posted: 6/19/2002 3:05:03 PM EDT
Originally Posted By The_Macallan: THIS is what I was taught to do with "x.5" * If x is an even number, round x.5 down, * If y is an even number, round x.5 up. In other words, always round x.5 to the nearest EVEN NUMBER! 3.5 rounds to 4 4.5 rounds to 4
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ERR, MAC, That is the correct way to round. The reason being, that it minimizes bias in systems. Since any system won't normally show a preponderence towards even or odd numbers, rounding the .5 to the nearest even number statistically evens out that about 50 percent of numbers will gain .5 and 50 percent will lose .5 . Of course, you could round to the nearest odd number with the same result, so long as you are consistant. -legrue
Link Posted: 6/19/2002 3:07:48 PM EDT
Link Posted: 6/19/2002 3:13:21 PM EDT
[Last Edit: 6/19/2002 3:16:22 PM EDT by Benjamin0001]
ERR, MAC, That is the correct way to round. The reason being, that it minimizes bias in systems. Since any system won't normally show a preponderence towards even or odd numbers, rounding the .5 to the nearest even number statistically evens out that about 50 percent of numbers will gain .5 and 50 percent will lose .5 . Of course, you could round to the nearest odd number with the same result, so long as you are consistant.
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Hahahah, mathematically speaking that works out but does it have any real world consequences?? I doubt it. [size=4] DOWN WITH ODD NUMBER RACISM!! DOWN WITH ODD NUMBER RACISM!! FREE THE ODD NUMBER!!!UNIVERSAL SUFFRAGE FOR ODD NUMBERS!!!ODD NUMBERS HAVE RIGHTS TO!!![size=4]
Link Posted: 6/19/2002 3:20:46 PM EDT
i was taught lots of wrong things in school. i went to catholic school, and thinking back, man, there was a lot of bullshit that we swallowed, hook, line and sinker.
Link Posted: 6/19/2002 3:28:11 PM EDT
Originally Posted By Benjamin0001:
ERR, MAC, That is the correct way to round. The reason being, that it minimizes bias in systems. Since any system won't normally show a preponderence towards even or odd numbers, rounding the .5 to the nearest even number statistically evens out that about 50 percent of numbers will gain .5 and 50 percent will lose .5 . Of course, you could round to the nearest odd number with the same result, so long as you are consistant.
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Hahahah, mathematically speaking that works out but does it have any real world consequences?? I doubt it. [size=4] DOWN WITH ODD NUMBER RACISM!! DOWN WITH ODD NUMBER RACISM!! FREE THE ODD NUMBER!!!UNIVERSAL SUFFRAGE FOR ODD NUMBERS!!!ODD NUMBERS HAVE RIGHTS TO!!![size=4]
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If I can stop laughing long enough to answer, yes, it has real world consequences. As to being an authority, I don't claim it, however IF I remember correctly, that was what was in my ASTM standards manual, what I was taught in my math classes, and what I used to audit laboratories to. -legrue [:)]
Link Posted: 6/19/2002 3:32:04 PM EDT
That when we graduated HS and enrolled in college, our education would be unbiased and free of political agendas.
Link Posted: 6/19/2002 3:45:48 PM EDT
Originally Posted By legrue: ERR, MAC, That is the correct way to round. The reason being, that it minimizes bias in systems. Since any system won't normally show a preponderence towards even or odd numbers, rounding the .5 to the nearest even number statistically evens out that about 50 percent of numbers will gain .5 and 50 percent will lose .5 . Of course, you could round to the nearest odd number with the same result, so long as you are consistant. -legrue
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My error in my original post. It should read: "In other words, always round x.5 to the [s]nearest[/s] [red]largest[/b] EVEN NUMBER!" So if 3.5, 3.6, 3.7, 3.8, 3.9, 4.1, 4.2, 4.3, 4.4 and 4.5 all round to 4 and 4.6, 4.7, 4.8, 4.9, 5.1, 5.2, 5.3, and 5.4 round to 5 (with 5.5 rounding to 6) then that's EIGHT numbers that round to 5 and TEN numbers that round to 4!
Link Posted: 6/19/2002 3:47:14 PM EDT
[Last Edit: 6/19/2002 3:52:42 PM EDT by Benjamin0001]
-------------------------------------------------------------------------------- Originally Posted By Benjamin0001: -------------------------------------------------------------------------------- ERR, MAC, That is the correct way to round. The reason being, that it minimizes bias in systems. Since any system won't normally show a preponderence towards even or odd numbers, rounding the .5 to the nearest even number statistically evens out that about 50 percent of numbers will gain .5 and 50 percent will lose .5 . Of course, you could round to the nearest odd number with the same result, so long as you are consistant. -------------------------------------------------------------------------------- Hahahah, mathematically speaking that works out but does it have any real world consequences?? I doubt it. DOWN WITH ODD NUMBER RACISM!! DOWN WITH ODD NUMBER RACISM!! FREE THE ODD NUMBER!!!UNIVERSAL SUFFRAGE FOR ODD NUMBERS!!!ODD NUMBERS HAVE RIGHTS TO!!! -------------------------------------------------------------------------------- If I can stop laughing long enough to answer, yes, it has real world consequences. As to being an authority, I don't claim it, however IF I remember correctly, that was what was in my ASTM standards manual, what I was taught in my math classes, and what I used to audit laboratories to.
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I am sure that in a system or group of solved problems where there are multiple problems for one solution it would help distribute the error throughout.. But the image I had is this poor kid in this classroom having to do 50 problems and going back and checking his answers to make sure that exactly 25 of them rounded one way and exactly 25 rounded the other way... . And now that I am looking at it we see another mathematical theory that we can pull out of just my paragraph... In exactly 50 numbers there will be exactly 25 even number and 25 odd numbers???? Hmmm, prove that one... Mr Legrue Smarty Pants!!!! {x:x>=1,x<=50,x<>0} Ben
Link Posted: 6/19/2002 3:49:56 PM EDT
Link Posted: 6/19/2002 3:56:27 PM EDT
I remember a health teacher in 8th grade telling us that cocaine comes from South Africa. I corrected her, saying she meant South America. She glared at me and asked who the teacher was in this class.
Link Posted: 6/19/2002 4:01:05 PM EDT
Originally Posted By Benjamin0001:
ERR, MAC, That is the correct way to round. The reason being, that it minimizes bias in systems. Since any system won't normally show a preponderence towards even or odd numbers, rounding the .5 to the nearest even number statistically evens out that about 50 percent of numbers will gain .5 and 50 percent will lose .5 . Of course, you could round to the nearest odd number with the same result, so long as you are consistant.
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Hahahah, mathematically speaking that works out but does it have any real world consequences?? I doubt it. [size=4] DOWN WITH ODD NUMBER RACISM!! DOWN WITH ODD NUMBER RACISM!! FREE THE ODD NUMBER!!!UNIVERSAL SUFFRAGE FOR ODD NUMBERS!!!ODD NUMBERS HAVE RIGHTS TO!!![size=4]
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[url]http://mathworld.wolfram.com/RoundoffError.html[/url]
The Patriot missile defense system used during the Gulf War was also rendered ineffective due to roundoff error (Skeel 1992, U.S. GAO 1992). The system used an integer timing register which was incremented at intervals of 0.1 s. However, the integers were converted to decimal numbers by multiplying by the binary approximation of 0.1, [img]http://mathworld.wolfram.com/rimg3281.gif[/img] As a result, after 100 hours ( [img]http://mathworld.wolfram.com/rimg3282.gif[/img]), an error of [img]http://mathworld.wolfram.com/rimg3283.gif[/img] had accumulated. This discrepancy caused the Patriot system to continuously recycle itself instead of targeting properly. As a result, an Iraqi Scud missile could not be targeted and was allowed to detonate on a barracks, killing 28 people.
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No real world consequences huh?
Link Posted: 6/19/2002 4:05:53 PM EDT
[Last Edit: 6/19/2002 4:06:16 PM EDT by AlClenin]
Originally Posted By Benjamin0001: In exactly 50 numbers there will be exactly 25 even number and 25 odd numbers???? Hmmm, prove that one... Mr Legrue Smarty Pants!!!! {x:x>=1,x<=50,x<>0} Ben
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You're wrong! I choose the following 50 numbers, all of which are contained in your set ({x:x>=1,x<=50,x<>0}) and none of which are even: 1.1, 1.2, 1.3, . . . , 1.50 Public school teacher were you?
Link Posted: 6/19/2002 4:08:36 PM EDT
By the way, as a definition of even number, I use: An integer of the form 2*n, where n is an integer.
Link Posted: 6/19/2002 4:17:07 PM EDT
Originally Posted By More_Cowbell: I remember a health teacher in 8th grade telling us that cocaine comes from South Africa. I corrected her, saying she meant South America. She glared at me and asked who the teacher was in this class.
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Maybe she simply got "cocaine" confused with "flaming, gasoline-soaked tires hung around the necks of your anti-marxist political adversaries".
Link Posted: 6/19/2002 4:44:54 PM EDT
"Living Document"
Link Posted: 6/19/2002 4:45:11 PM EDT
I went to a fundamentalist baptist school so I was CONSTANTLY taught wrong in science and Bible class. But I gotta admit that Algebra class was fun...the teacher was more interested in talking about SWAPO and UNITA and Communist geurillas in Africa than Algebra, so with just a little effort we could get him off on a tangent that would last all class long...
Link Posted: 6/19/2002 4:45:50 PM EDT
Originally Posted By AlClenin:
Originally Posted By Benjamin0001: In exactly 50 numbers there will be exactly 25 even number and 25 odd numbers???? Hmmm, prove that one... Mr Legrue Smarty Pants!!!! {x:x>=1,x<=50,x<>0} Ben
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You're wrong! I choose the following 50 numbers, all of which are contained in your set ({x:x>=1,x<=50,x<>0}) and none of which are even: 1.1, 1.2, 1.3, . . . , 1.50 Public school teacher were you?
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Ouch, he got ya a good one, Ben! For the problem you probably intended, I would have to dust off some long dormant brain cells. Still, I'll think about the proof [:D] -legrue
Link Posted: 6/19/2002 5:01:35 PM EDT
The economics teacher across from my study hall is constantly deriding globalization, saying that it's evil, etc. Definitly a socialist. He also has bumber stickers on his car that say "Indians were the first Americans" and a handgun with an "x" through it (like the no smoking sign) [rolleyes]. I really hope I don't have him for AP Economics in 12th grade.
Link Posted: 6/19/2002 5:06:37 PM EDT
Originally Posted By The_Macallan: So if 3.5, 3.6, 3.7, 3.8, 3.9, 4.1, 4.2, 4.3, 4.4 and 4.5 all round to 4 and 4.6, 4.7, 4.8, 4.9, 5.1, 5.2, 5.3, and 5.4 round to 5 then that's EIGHT numbers that round to 5 and TEN numbers that round to 4!
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Correct.
Link Posted: 6/19/2002 5:19:10 PM EDT
[Last Edit: 6/19/2002 5:20:07 PM EDT by Benjamin0001]
hahahaha, I knew where the Whole was....... hahaha [:I] Okay how about this: And yes, ALCLENIN, I did say this: so we are not mistaken. BENJAMIN WROTE BEFORE ALCLENIN:
I am sure that in a system or group of solved problems where there are multiple problems for one solution it would help distribute the error throughout
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But I have to admit that I only can shave by on that statment. Yes, I remember the Patriot problem with rounding errors due on the TimeBase. Okay let me restate this problem. {x:x is an element of L(natural numbers),} Prove that , for any "CONSECUTIVE Natural Numbers" numbering 50 there are exactly 25 odds and 25 even "Natural Numbers". There, that takes out the ambiguity.. Takle that one Alclenin.. And I want the Proof, not an example. Ben Slip through that one
Link Posted: 6/19/2002 5:40:57 PM EDT
[Last Edit: 6/19/2002 6:45:26 PM EDT by AlClenin]
Originally Posted By Benjamin0001: hahahaha, I knew where the Whole was....... hahaha [:I] Okay how about this: And yes, ALCLENIN, I did say this: so we are not mistaken. BENJAMIN WROTE BEFORE ALCLENIN:
I am sure that in a system or group of solved problems where there are multiple problems for one solution it would help distribute the error throughout
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Not sure what that means.
But I have to admit that I only can shave by on that statment. Yes, I remember the Patriot problem with rounding errors due on the TimeBase. Okay let me restate this problem. {x:x is an element of L(natural numbers),} Prove that , for any "CONSECUTIVE Natural Numbers" numbering 50 there are exactly 25 odds and 25 even "Natural Numbers".
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Proof by mathematical induction (informal) Let i be the first number in any set of 50 consecutive natural numbers. When i = 1 the conjecture is obviously true. In this case the numbers are 1,2, ...,50. Simply write them all down and examine them and you'll see that 25 are odd and 25 are even. Suppose the statement holds true for i=n. This means that you have the consecutive natural numbers n,n+1,n+2,...,n+49 and that exactly 25 of these are odd and exactly 25 are even. Suppose n is even, then n+1 is odd, n+2 is even and so on with n+49 being odd. Take n out of this set of numbers, leaving n+1, n+2, ..., n+49. Now you have 49 numbers with exactly 24 even and 25 odd. Now add in n+50, which must be even since n+49 is odd. This shows that n+1, n+2, ..., n+50 has exactly 25 odd and 25 even numbers. That is, the statement holds true when i = n+1 and n is even. An analagous argument will show that the statement holds true for i = n+1 when n is odd. Thus we see that the statement is true for i=1, and that if it is true for i=n, then it must also be true for i = n + 1. Therefore it is true for all natural numbers i.
Link Posted: 6/19/2002 6:26:37 PM EDT
[Last Edit: 6/19/2002 6:36:57 PM EDT by Benjamin0001]
So what you are really saying is. If 50-1=49 and the addends of 49 are 24 and 25 then 24 of them even and 25 of them are odd Very creative.... Hahahah. Shit Al Clenin, time to brush up on the Math, your batting out of my league. Ben
Link Posted: 6/19/2002 6:47:54 PM EDT
[Last Edit: 6/19/2002 6:52:15 PM EDT by jz02]
There is a nicer way to do a proof. Consider the definition of odd and even, we may restate it as ODD is congruent to 1 mod 2, EVEN is congruent to 0 mod 2. Since these are the only numbers in mod 2, we may represent all integers as 0 or 1 in mod 2. We know that no two consequtive integers can have the same least residue in any non-trivial mod. So in any number of consequtive group of integers, at most half will be even or odd. Since we know that the number of even or odd in any given group of consequtive integers is less than or equal to half the number, and that the number of even or odd have to add up to that number, we can conclude that both are exactly half. (rounded) If there's more than half of either odd or even, then we run into the pigeon hole principal since there can't be consequtive odds or evens.
Link Posted: 6/19/2002 6:58:26 PM EDT
Originally Posted By legrue: ERR, MAC, That is the correct way to round.
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Are you sure??? Doesn't seem like it to me!
Link Posted: 6/19/2002 6:58:47 PM EDT
Originally Posted By jz02: There is a nicer way to do a proof. Consider the definition of odd and even, we may restate it as ODD is congruent to 1 mod 2, EVEN is congruent to 0 mod 2. Since these are the only numbers in mod 2, we may represent all integers as 0 or 1 in mod 2. We know that no two consequtive integers can have the same least residue in any non-trivial mod. So in any number of consequtive group of integers, at most half will be even or odd. Since we know that the number of even or odd in any given group of consequtive integers is less than or equal to half the number, and that the number of even or odd have to add up to that number, we can conclude that both are exactly half. (rounded) If there's more than half of either odd or even, then we run into the pigeon hole principal since there can't be consequtive odds or evens.
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Induction was the first thing that poped into my head. I haven't dealt with modular arithmetic very much. I think induction would be easier to explain to a non-mathematical crowd.
Link Posted: 6/19/2002 7:04:08 PM EDT
well my proof doesn't really hinge on modular arithmetic. You can start with any general premise that will demonstrate that no two odd or evens can be consequtive. Once you have that down my proof is the typical less than or equal to and greater than or equal to therefore equal proof. Since both are less than or equal to half and they have to add up to the total(therefore greater than or equal to half), they're both equal to half. I find this more intuitive in this case. I find it easier to visualize induction(which is helpful in other proofs), but my proof is more intuitive to me logically in this case.
Link Posted: 6/19/2002 7:26:21 PM EDT
Link Posted: 6/19/2002 7:28:24 PM EDT
Originally Posted By The_Macallan:
Originally Posted By legrue: ERR, MAC, That is the correct way to round.
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Are you sure??? Doesn't seem like it to me!
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Yeah, fairly sure. An ASTM manual with the statistical methods would tell you for sure, but as I recall that is the correct method. Just consider if you have a random distribution of data points and each needs to be rounded to a given accuracy. Say you are then going to add them up and calculate the mean value. If you are always rounding the .5 up (or down) you are introducing a bias up (or down). If your data points are truely random, then rounding the .5 to the nearest even (or odd) avoids the bias. If anyone has the ASTM method handy, I'm all ears. All my books are at an old job :) -legrue
Link Posted: 6/19/2002 7:57:10 PM EDT
Originally Posted By legrue:
Originally Posted By The_Macallan:
Originally Posted By legrue: ERR, MAC, That is the correct way to round.
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Are you sure??? Doesn't seem like it to me!
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Yeah, fairly sure. An ASTM manual with the statistical methods would tell you for sure, but as I recall that is the correct method. Just consider if you have a random distribution of data points and each needs to be rounded to a given accuracy. Say you are then going to add them up and calculate the mean value. If you are always rounding the .5 up (or down) you are introducing a bias up (or down). If your data points are truely random, then rounding the .5 to the nearest even (or odd) avoids the bias. If anyone has the ASTM method handy, I'm all ears. All my books are at an old job :) -legrue
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So if 3.5, 3.6, 3.7, 3.8, 3.9, 4.1, 4.2, 4.3, 4.4 and 4.5 all round to 4 and 4.6, 4.7, 4.8, 4.9, 5.1, 5.2, 5.3, and 5.4 round to 5 (with 5.5 rounding to 6) then that's EIGHT numbers that round to 5 and TEN numbers that round to 4! That's HARDLY "unbiased" in distribution of those numbers. BUT... if 3.5 3.6, 3.7, 3.8, 3.9, 4.1, 4.2, 4.3, 4.4 all round to 4 (with 4.5 rounding to 5) and 4.5, 4.6, 4.7, 4.8, 4.9, 5.1, 5.2, 5.3, and 5.4 round to 5 (with 5.5 rounding to 6) then that's NINE numbers that round to 5 and NINE numbers that round to 4! That seems more "unbiased" in distribution of those same numbers.
Link Posted: 6/19/2002 8:39:35 PM EDT
Originally Posted By The_Macallan: So if 3.5, 3.6, 3.7, 3.8, 3.9, 4.1, 4.2, 4.3, 4.4 and 4.5 all round to 4 and 4.6, 4.7, 4.8, 4.9, 5.1, 5.2, 5.3, and 5.4 round to 5 (with 5.5 rounding to 6) then that's EIGHT numbers that round to 5 and TEN numbers that round to 4! That's HARDLY "unbiased" in distribution of those numbers. BUT... if 3.5 3.6, 3.7, 3.8, 3.9, 4.1, 4.2, 4.3, 4.4 all round to 4 (with 4.5 rounding to 5) and 4.5, 4.6, 4.7, 4.8, 4.9, 5.1, 5.2, 5.3, and 5.4 round to 5 (with 5.5 rounding to 6) then that's NINE numbers that round to 5 and NINE numbers that round to 4! That seems more "unbiased" in distribution of those same numbers.
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No, not the right math or spread. Consider the same numbers: 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 round down, 5 round up 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 round down, 4 round up The intervals between the units being rounded to is what you want to look at. In this example, if you know your number will randomly fall between 3 and 5, it has a 50/50 chance of being in the 3-4 interval and the same chance of being in the 4-5 interval. The final rounded number will be a 3, a 4, or a 5, not a 3.5, or 4.5. By extension, if the only two choices become 3.5 or 4.5, then given a sufficently large number of data for a gaussian distribution, you will average 50% on 3.5 and 50% on 4.5 and no bias. As I mentioned earlier, restrictions on data sets can indeed introduce bias with this rounding and must be taken into account. -legrue
Link Posted: 6/19/2002 9:07:03 PM EDT
Originally Posted By AlClenin:
Originally Posted By Benjamin0001:
ERR, MAC, That is the correct way to round. The reason being, that it minimizes bias in systems. Since any system won't normally show a preponderence towards even or odd numbers, rounding the .5 to the nearest even number statistically evens out that about 50 percent of numbers will gain .5 and 50 percent will lose .5 . Of course, you could round to the nearest odd number with the same result, so long as you are consistant.
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Hahahah, mathematically speaking that works out but does it have any real world consequences?? I doubt it. [size=4] DOWN WITH ODD NUMBER RACISM!! DOWN WITH ODD NUMBER RACISM!! FREE THE ODD NUMBER!!!UNIVERSAL SUFFRAGE FOR ODD NUMBERS!!!ODD NUMBERS HAVE RIGHTS TO!!![size=4]
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[url]http://mathworld.wolfram.com/RoundoffError.html[/url]
The Patriot missile defense system used during the Gulf War was also rendered ineffective due to roundoff error (Skeel 1992, U.S. GAO 1992). The system used an integer timing register which was incremented at intervals of 0.1 s. However, the integers were converted to decimal numbers by multiplying by the binary approximation of 0.1, [img]http://mathworld.wolfram.com/rimg3281.gif[/img] As a result, after 100 hours ( [img]http://mathworld.wolfram.com/rimg3282.gif[/img]), an error of [img]http://mathworld.wolfram.com/rimg3283.gif[/img] had accumulated. This discrepancy caused the Patriot system to continuously recycle itself instead of targeting properly. As a result, an Iraqi Scud missile could not be targeted and was allowed to detonate on a barracks, killing 28 people.
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No real world consequences huh?
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I hated Math in school and I still hate math today and boy am I ignorant and when I read stuff like this I hate being ignorant too! [xx(]
Link Posted: 6/19/2002 9:15:33 PM EDT
Originally Posted By legrue: No, not the right math or spread. Consider the same numbers: 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 round down, 5 round up 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 round down, 4 round up The intervals between the units being rounded to is what you want to look at. In this example, if you know your number will randomly fall between 3 and 5, it has a 50/50 chance of being in the 3-4 interval and the same chance of being in the 4-5 interval. The final rounded number will be a 3, a 4, or a 5, not a 3.5, or 4.5. By extension, if the only two choices become 3.5 or 4.5, then given a sufficently large number of data for a gaussian distribution, you will average 50% on 3.5 and 50% on 4.5 [red]and no bias.[/red] As I mentioned earlier, restrictions on data sets can indeed introduce bias with this rounding and must be taken into account. -legrue
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"...and no bias"?? Okay now I'm even more confused. In your example, 10/18 (55.56%) of the numbers will round to 4 including both 3.5 and 4.5 Isn't that bias??
Link Posted: 6/19/2002 9:18:37 PM EDT
was i ever taught wrong in school? A:private school (yes) B:public School (well DUH! yes) c: home school! (no)
Link Posted: 6/19/2002 9:29:22 PM EDT
That Patriot missile bug is a real doosy because one would expect better smarts from the people writing those kinds of programs, especially anything having to do with the manipulation of floating point numbers in computer systems. The FIRST stinkin' thing you learn in school is floating point numbers are stored as an approximation. If you need absolute precision, you used fixed-point representations such as BCD. Hell, IBM mainframes had special registers for BCD because they were losing pennies in their accounting systems. And that was the 1960's for God's sake. Anyway, if they really lost precision as the result of using floating-point registers or emulation, it's a sorry state of affairs in the defense industry. Hell, everyone in computer science knows 0.1 + 0.1 + 0.1 - 0.1 - 0.1 - 0.1 doesn't always equal zero!
Link Posted: 6/19/2002 9:38:07 PM EDT
Originally Posted By legrue:
Originally Posted By The_Macallan: So if 3.5, 3.6, 3.7, 3.8, 3.9, 4.1, 4.2, 4.3, 4.4 and 4.5 all round to 4 and 4.6, 4.7, 4.8, 4.9, 5.1, 5.2, 5.3, and 5.4 round to 5 (with 5.5 rounding to 6) then that's EIGHT numbers that round to 5 and TEN numbers that round to 4! That's HARDLY "unbiased" in distribution of those numbers. BUT... if 3.5 3.6, 3.7, 3.8, 3.9, 4.1, 4.2, 4.3, 4.4 all round to 4 (with 4.5 rounding to 5) and 4.5, 4.6, 4.7, 4.8, 4.9, 5.1, 5.2, 5.3, and 5.4 round to 5 (with 5.5 rounding to 6) then that's NINE numbers that round to 5 and NINE numbers that round to 4! That seems more "unbiased" in distribution of those same numbers.
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No, not the right math or spread. Consider the same numbers: 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 round down, 5 round up 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 round down, 4 round up The intervals between the units being rounded to is what you want to look at. In this example, if you know your number will randomly fall between 3 and 5, it has a 50/50 chance of being in the 3-4 interval and the same chance of being in the 4-5 interval. The final rounded number will be a 3, a 4, or a 5, not a 3.5, or 4.5. By extension, if the only two choices become 3.5 or 4.5, then given a sufficently large number of data for a gaussian distribution, you will average 50% on 3.5 and 50% on 4.5 and no bias. As I mentioned earlier, restrictions on data sets can indeed introduce bias with this rounding and must be taken into account. -legrue
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[stick]STOP IT, PLEASE MY HEAD HURTS[stick]
Link Posted: 6/19/2002 9:51:43 PM EDT
Well, in response to the original question.... I started learning math in a catholic school in 1962. We learned "new math" What a goat F**K! My parents never got it... I simply watched them do in 4 operations what I was being taught to do in 12. Does that count?
Link Posted: 6/19/2002 10:04:48 PM EDT
Originally Posted By Sweep:
Originally Posted By Ponyboy: What about my highschool history teacher trying to tell me that the Civil War was only fought to free the slaves? I knew better even back then.
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I was watching C-SPAN the other night and this guy was saying that it actually wasn't a civil war. By definition a civil war is between two fractions of a country fighting for the power to rule the whole country. The South didn't want to rule the North, they just didn't want anything to do with it. Makes sense to me. Anyone concur? Besides, I like "The war of Northern Agression" better anyway! [:D]
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I'll back you on that. Hmmmm... My dictionary says that a civil war is "a war between political factions or regions within the same country." So whether it is a civil war depends on if you consider the South's secession to be legitimate. Aw heck, guess I need a new dictionary, I still like your definition better.
Link Posted: 6/19/2002 10:17:18 PM EDT
What was the question? I'm so confused.
Link Posted: 6/19/2002 10:32:45 PM EDT
teacher could you repeat the question, i was sleeping [sleep]
Link Posted: 6/19/2002 10:41:54 PM EDT
Originally Posted By Ponyboy: What about my highschool history teacher trying to tell me that the Civil War was only fought to free the slaves? I knew better even back then.
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As a matter of fact, the civil war was fought for states rights. Keving67
Link Posted: 6/19/2002 11:49:52 PM EDT
I was taught that the "Bill of Rights" meant something, guess they were wrong!
Link Posted: 6/20/2002 5:06:39 AM EDT
They caught the peasant walking home from the field. On the dark road they gagged him and cut off his nose. This they took to the museum and stuck to the king's noseless statue. Thus was born the history that is taught in schools. - Amitava Kumar, "History"
Link Posted: 6/20/2002 6:18:49 AM EDT
Originally Posted By The_Macallan: "...and no bias"?? Okay now I'm even more confused. In your example, 10/18 (55.56%) of the numbers will round to 4 including both 3.5 and 4.5 Isn't that bias??
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We have a set of numbers: 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 Avg: 4 Our set rounded as explained: 3 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 5 Avg: 4 Now where 5 rounds up exclusively: 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 Avg: 4.055555555... It seems a bit odd but it all comes down to keeping accuracy while losing precision.
Link Posted: 6/20/2002 6:53:18 AM EDT
Link Posted: 6/20/2002 7:02:44 AM EDT
Originally Posted By Jetlag:
Originally Posted By The_Macallan: "...and no bias"?? Okay now I'm even more confused. In your example, 10/18 (55.56%) of the numbers will round to 4 including both 3.5 and 4.5 Isn't that bias??
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We have a set of numbers: 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 Avg: 4 Our set rounded as explained: 3 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 5 Avg: 4 Now where 5 rounds up exclusively: 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 Avg: 4.055555555... It seems a bit odd but it all comes down to keeping accuracy while losing precision.
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Muchas Gracias. I was thinking of a way to explain it easier this morning in the shower (sad, I know). Easiest way I came up with was this: Since the only numbers we really care about are the x.5's, throw out the rest. Now assume the data is random. That is, x.5 doesn't occur preferentially between say, 4 and 5, but anywhere and everywhere. If you always add a .5 (round up) your average will be larger than the real average. Same logic if you always round .5 down. You need a way to round up for half of the x.5's and down for the other half. Since you can establish that half of the x.5's will statistically be below an even number and half will be above an even (due to random distribution), if you round to the even, it is a wash. (same logic if you consistantly round to an odd). My sincerest appologies to everyone else for having to witness that. -legrue
Link Posted: 6/20/2002 7:07:29 AM EDT
Originally Posted By Jetlag: It seems a bit odd but it all comes down to keeping accuracy while losing precision.
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Then why do spreadsheet programs always round .5 UP?
Link Posted: 6/20/2002 7:12:09 AM EDT
End the [b]odd[/b] discrimination! Down with [b]even[/b]! Round to the [b]odd[/b]! You know you want to. It's just as correct, IF NOT MORE CORRECT BECAUSE OF HISTORICAL DISCRIMINATION AGAINST ALL [b]ODDS[/b]! KILL [B]EVENY[/B]! KILL [b]EVENY[/b]!
Link Posted: 6/20/2002 7:14:25 AM EDT
[Last Edit: 6/20/2002 7:15:30 AM EDT by Jetlag]
Originally Posted By The_Macallan: Then why do spreadsheet programs always round .5 UP?
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I dunno, maybe because accountants are stupid? Seriously, though, they'd probably get more complaints about it than they'd like to handle.
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