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Maths Questions- absolute errors

kalen said:
What would be the equivalent "North American grade" or approximate age range of students learning this level material?
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You're normally 18 when you take A-Levels. It's an optional 2 year course that follows GCSEs (General Certificate of Secondary Education) taken at the age of 16. I have no idea what the US equivalent of that would be. The "A" stands for "Advanced", by the way.
 
BillHoyt said:
Excuse me. Soapy Sam is correct. The notion of errors is a measure-theoretic one, not an arithmetic one.
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I wouldn't use the expression "measure-theoretic" here. The notion of errors in this case has to do with measurements and instrumentation (and experimental design?), not measure theory (unless I missed something Lebesguesque in the question, after all, my knowledge of measure theory is minimal and very rusty).
 
Jorghnassen said:
I wouldn't use the expression "measure-theoretic" here. The notion of errors in this case has to do with measurements and instrumentation (and experimental design?), not measure theory (unless I missed something Lebesguesque in the question, after all, my knowledge of measure theory is minimal and very rusty).
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I'm not sure how you are viewing measurement theory. My viewpoint matches this:

"Measurement is the process of associating numbers with physical quantities and phenomena. The process is accomplished through the comparison of a measured value with some known quantity (standard) of the same kind. The subject has become of vital importance in sciences, engineering and to much everyday activity.

While measurement theory began with the Greeks in the 4th century BC, the first useful work appeared in the 18th century by English mathematician Thomas Simpson on observation error - perhaps the most important single aspect of measurement theory."

Definition

Simpson's first work was on observation error, which is the crux of the OP's question.
 
Letteth us not compoundeth our errors.

Shall we agree to settle for "Tolerance" ? :)



Ed to add:- Karen, the "11-16" is the intended age range. Junior high.
 
TeaBag420 said:
One of you is saying "measure theory" and the other is saying "measurement theory".
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Yes. What I meant was that BillyHoyt should have said "measurement-theoretic", not "measure-theoretic". Because those two aren't the same thing.
 
Jorghnassen said:
Yes. What I meant was that BillyHoyt should have said "measurement-theoretic", not "measure-theoretic". Because those two aren't the same thing.
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No offense, Joghnassen, but the roots are the same. Stochastic processes drive one of the two principal error classes.
 
Re: Re: Re: Maths Questions- absolute errors

Art Vandelay said:
When you multiply two numbers together, the rule is that you multiply the error of one number by the other number (taking absolute values, of course). In this case, the error would be (x error)*y+(y error)*x=.37*4.291+.291*537~=3.2.
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Shouldn't you do this for both (x error)*y+(y error) and for (y error)*x+(x error)? I would think the error in this case is the larger of the two values?
 
BillHoyt said:
No offense, Joghnassen, but the roots are the same. Stochastic processes drive one of the two principal error classes.
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None taken. It's just that for someone with a little pure math background like me, measure theory means sigma-algebras and Banach spaces, is all about abstract structures and has nothing to do with measurements of anything concrete...

/now I have a headache from trying to remember probability theory.
 
Of course this is an ambiguous (or "multiguous") problem. But it's a math test, and they're probably just looking for a simple-minded answer that shows a basic understanding of what a significant figure is, which is described at http://www.counton.org/alevel/pure/purtutnumerr.htm

Of course any scientist or statistician who calculated errors this way should be taken out and shot, but I don't think that's what they're looking for.
 
BillHoyt said:
No offense, Joghnassen, but the roots are the same. Stochastic processes drive one of the two principal error classes.
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By "roots", do you mean the etymological roots? Are you saying that measure theory is stochastic? Measure theory relates one mathematical construct to another. Measurement theory relates physical constructs to mathematical ones. They are of very different natures.

Harlequin
Shouldn't you do this for both (x error)*y+(y error) and for (y error)*x+(x error)? I would think the error in this case is the larger of the two values?
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I'm not sure what you mean. Do you mean the error is max[ (x error)*y+(y error), (y error)*x+(x error) ]?
 
Art Vandelay said:
By "roots", do you mean the etymological roots? Are you saying that measure theory is stochastic? Measure theory relates one mathematical construct to another. Measurement theory relates physical constructs to mathematical ones. They are of different natures.
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Art,

Measure theory is the study of lengths, area, and volume. It is closely related to integration, another solution to relating mathematical constructs to physical constructs. And, yes, measure theory is a foundational framework for probability theory.
 
BillHoyt said:
Art,

Measure theory is the study of lengths, area, and volume. It is closely related to integration, another solution to relating mathematical constructs to physical constructs. And, yes, measure theory is a foundational framework for probability theory.
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I think that:

a. you're wrong, and

b. you're regoogletating something you found on the internet, without reading it thoroughly or with the appropriate background knowledge.
 
TeaBag420 said:
I think that:

a. you're wrong, and

b. you're regoogletating something you found on the internet, without reading it thoroughly or with the appropriate background knowledge.
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*yawn* Mosquito season again, eh?
 
BillHoyt said:
Measure theory is the study of lengths, area, and volume. It is closely related to integration, another solution to relating mathematical constructs to physical constructs. And, yes, measure theory is a foundational framework for probability theory.
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I think that there is a distinction between the length/area/volume of a mathetical construct and the length/area/volume of a physical object. Mixing them up is what causes people to think that they can cut an orange into a bunch of pieces and put them back together into something with more volume than the original orange. In a similar vein, integration relates functions to mathematical area. Measurement theory deals with how to get the function from physical quantities. Calculus takes the function as a given, and does not deal with the underlying physical quantities represented. And while stochastic processes involve measure theory, I don't think that means that measure theory is stochastic.
 
Soapy Sam said:
"No number is 100% exact."- New DRKitten


I beg to differ.

All numbers are 100% exact or we can kiss arithmetic (and thence mathematics) farewell.

No quantity is exact. Measurement has inherent error and is performed with known tolerances.

If x is 5.37, then x is 5.37, no more, no less, if it was arrived at mathematically. (6.37 minus 1 is 5.37 and no noodging. If $5.37 is my change, I want no.005c coins, thanks.)

If they derived the 5.37 by slapping a tape on a board and marking it with a grease pencil, well thats another kettle of crustaceans entirely.

This is the sort of thing that happens when mathematicians try to write English. It should be stamped on hard, by all right thinking persons.
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But...5.37 is only exact if the person tells you it is exact. Not by simply looking at that number!

Suppose, in actuality, it is 5 .37490643982756475. This number would round off to 5.37 if the person chose to terminate the number at 1/100ths.

Answer me this: Suppose there is a car race on the quarter mile track. One car made a run of 5.37 seconds. But the other ran an ET of 5.374. Who won the race? Unless you knew the *exact time*, determined by who broke the light beam through the traps, you really wouldn't know.

We can fairly say that in determining time, with numbers, that we can't do any better than the speed of light. And to get that exact number, would require many many numbers beyond the decimal point. Not just 2 numbers past the decimal point.


But, if someone said the number was 5.37000000, instead of 5.37...that would be very different.
 
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