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Posted: 6/19/2002 1:48:08 PM EST
[Last Edit: 6/19/2002 2:46:49 PM EST 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 mathrelated 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.


I am not the means to any end others may wish to accomplish. I am not a tool for their use. I do not surrender my treasures to be flung to the winds as alms for the poor.
~ From "Anthem" 
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.


www.hogzillascents.com
www.wildhoghunters.com 
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]



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
View Quote 


Below 5, round down. 5 and above, round up.
Wonder if anybody could give us a definitve answer, if there is one?


That's PERSEC, not OPSEC. AvengeR15

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.
View Quote 


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.



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.
View Quote View Quote 


That when we graduated HS and enrolled in college, our education would be unbiased and free of political agendas.


"Okay, but I'm not good at details, or the big picture. I also show up late, and drunk. I've got a good feeling about this."
 Homer Simpson 
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
View Quote 

I am not the means to any end others may wish to accomplish. I am not a tool for their use. I do not surrender my treasures to be flung to the winds as alms for the poor.
~ From "Anthem" 

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.
View Quote 


Were you ever taught wrong in school... View Quote 

"How long has it been since we've flown through shadows?
I have walked on many other planets..." 
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.



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.
View Quote View Quote 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. View Quote 


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 View Quote 


By the way, as a definition of even number, I use: An integer of the form 2*n, where n is an integer.



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. View Quote 

I am not the means to any end others may wish to accomplish. I am not a tool for their use. I do not surrender my treasures to be flung to the winds as alms for the poor.
~ From "Anthem" 
"Living Document"


Always Think Forfeiture
My right to keep and bear weapons of mass destruction shall not be infringed! 
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...


The first part of your life, you worry about what people think about you;
The middle part of your life, you don't care what people think about you; The last part of your life, you realize they weren't even thinking about you at all. 
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 View Quote View Quote 


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.



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!
View Quote 

Always Think Forfeiture
My right to keep and bear weapons of mass destruction shall not be infringed! 
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
View Quote 


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
View Quote View Quote
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". View Quote 


So what you are really saying is.
If 501=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



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 nontrivial 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.



Originally Posted By legrue:
ERR, MAC,
That is the correct way to round. View Quote 

I am not the means to any end others may wish to accomplish. I am not a tool for their use. I do not surrender my treasures to be flung to the winds as alms for the poor.
~ From "Anthem" 
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 nontrivial 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. View Quote 


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.



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. View Quote 

Why buy the cow when the neighbor's cat is in heat?

Originally Posted By The_Macallan:
Originally Posted By legrue:
ERR, MAC,
That is the correct way to round. View Quote View Quote 


Originally Posted By legrue:
Originally Posted By The_Macallan:
Originally Posted By legrue:
ERR, MAC,
That is the correct way to round. View Quote View Quote View Quote 

I am not the means to any end others may wish to accomplish. I am not a tool for their use. I do not surrender my treasures to be flung to the winds as alms for the poor.
~ From "Anthem" 
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. View Quote 


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.
View Quote View Quote 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. View Quote View Quote 


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 34 interval and the same chance of being in the 45 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 View Quote 

I am not the means to any end others may wish to accomplish. I am not a tool for their use. I do not surrender my treasures to be flung to the winds as alms for the poor.
~ From "Anthem" 
was i ever taught wrong in school?
A:private school (yes)
B:public School (well DUH! yes)
c: home school! (no)


[NO TEXT]

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 fixedpoint 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 floatingpoint 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!


"Okay, but I'm not good at details, or the big picture. I also show up late, and drunk. I've got a good feeling about this."
 Homer Simpson 
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. View Quote View Quote 


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?



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. View Quote View Quote 


What was the question?
I'm so confused.


343
Never Forget كافر 
teacher could you repeat the question, i was sleeping [sleep]


[NO TEXT]

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. View Quote 


I was taught that the "Bill of Rights" meant something, guess they were wrong!



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"



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??
View Quote 

Always Think Forfeiture
My right to keep and bear weapons of mass destruction shall not be infringed! 
Yes I was taught wrong in school.
The theory of EVOLUTION !!![devil]


Originally Posted By EricTheHun
I think maybe you oughtta get yourself an M16 ~ Col Hal Moore Time comes I need one Sir, there'll be plenty of 'em lying on the ground ~ Sgt Maj Plumley ar15.com ar15armory.com thetreeofliberty.com 
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??
View Quote View Quote 


Originally Posted By Jetlag:
It seems a bit odd but it all comes down to keeping accuracy while losing precision.
View Quote 

I am not the means to any end others may wish to accomplish. I am not a tool for their use. I do not surrender my treasures to be flung to the winds as alms for the poor.
~ From "Anthem" 
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]!


Always Think Forfeiture
My right to keep and bear weapons of mass destruction shall not be infringed! 
Originally Posted By The_Macallan:
Then why do spreadsheet programs always round .5 UP?
View Quote 

Always Think Forfeiture
My right to keep and bear weapons of mass destruction shall not be infringed! 
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