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September 19th, 2012, 09:14 AM   #1
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Formulas

Hi - Can it be said that all mathematical formulas have only approximate solutions or just some? And if they do or do not, is there a rule of thumb to determine which? If you do not know, that is okay.
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September 19th, 2012, 09:37 AM   #2
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Re: Formulas

I'm not sure what you mean by approximate solutions, would you give an example?
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September 19th, 2012, 11:13 AM   #3
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Re: Formulas

Well, any formula with pi used in it, I would consider could give only an approximate result. Any formula that would result in non ending decimal fractions, I would consider an approximate result. Such as C = 2 pi r for the circumference of a circle. E = MC squared...the correct speed of light should be a non ending number and therefore the formula could only result in an estimate, correct? The normally used electrical Ohms law formulas are just 'close' working formulas. And these working figures are changed every so often, and again, these result in never ending decimal fractions. We are familiar with the endless decimal places that are usually rounded off for working simplicity. This is what I mean.
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September 19th, 2012, 02:40 PM   #4
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Re: Formulas

I honestly don't understand this fetish people have for terminating decimal numbers. What's so special about them?

Quote:
Originally Posted by yesiam
E = MC squared...the correct speed of light should be a non ending number and therefore the formula could only result in an estimate, correct?
Uh, no?

I don't think there's any reason to consider numbers with a strange property in decimal (you can write them out in a finite number of symbols) any special status, certainly no more than I'd accord numbers that have a finite ternary expansion. I'd consider them less important than numbers that can be written in a finite number of symbols in base-phi, where phi = (1+sqrt(5))/2.

What's wrong with an irrational number, or an algebraic one? We're not stuck in ancient Greece like Pythagoras.

But even for some bizarre reason we do care (in a very parochial way) about how our numbers look when written in base (1+1)*(1+1+1+1+1). We can't measure any fundamental physical constant -- or really anything -- to 20 decimal places. How do we decide if a number is a terminating decimal or not? We could never measure it precisely enough.
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September 19th, 2012, 04:42 PM   #5
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Re: Formulas

That's okay, I understand...
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September 19th, 2012, 06:01 PM   #6
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Re: Formulas

Quote:
Originally Posted by yesiam
Well, any formula with pi used in it, I would consider could give only an approximate result.
I think the answer to your question is that math and physics are different.

Math is concerned about math. In math when people write the number pi, they mean exactly pi. In math, irrational numbers exist.

In physics (and in physical reality in general) when scientists use a number to represent a measurement, that number is approximate. Because all physical measurement is approximate.

Note that this applies not only to irrational numbers like pi, but to all numbers. Can you measure exactly 1/2 meter? No you can't. The number 1/2 is just as approximate (in science) as the number pi. If you have 1 planet, then that's exact. But if you measure a bar of gold to be 1 kilogram, that 1 is approximate.

But again, in pure math, 1/2 and pi and all the other crazy numbers mathematicians use have exact values.
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September 19th, 2012, 10:43 PM   #7
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Re: Formulas

Maschke captured what I meant much better than I did.
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September 20th, 2012, 07:43 AM   #8
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Re: Formulas

Hi - I 'was' referring to 'mathematical formulas' as in I my question. Sorry I was misunderstood. I have always wondered about this and still don't know. I have a feeling that I may not be alone. Thanks for input.
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September 20th, 2012, 11:26 AM   #9
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Re: Formulas

I don't understand what you're asking, sorry.
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September 21st, 2012, 04:10 PM   #10
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Re: Formulas

Quote:
Originally Posted by yesiam
Well, any formula with pi used in it, I would consider could give only an approximate result. Any formula that would result in non ending decimal fractions, I would consider an approximate result. Such as C = 2 pi r for the circumference of a circle. E = MC squared...the correct speed of light should be a non ending number and therefore the formula could only result in an estimate, correct?
No, it is perfectly legitimate, and often done, to use units in which c= 1, exactly. And in the standard metric system, the meter is defined such that the speed of light is exactly 299,792,458 meters per second.

As others have pointed out, math and physics are not the same thing- but the speed of light is a very poor example!

Quote:
The normally used electrical Ohms law formulas are just 'close' working formulas. And these working figures are changed every so often, and again, these result in never ending decimal fractions. We are familiar with the endless decimal places that are usually rounded off for working simplicity. This is what I mean.
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