September 19th, 2012, 09:14 AM  #1 
Newbie Joined: Sep 2012 Posts: 4 Thanks: 0  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.

September 19th, 2012, 09:37 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Formulas
I'm not sure what you mean by approximate solutions, would you give an example?

September 19th, 2012, 11:13 AM  #3 
Newbie Joined: Sep 2012 Posts: 4 Thanks: 0  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.

September 19th, 2012, 02:40 PM  #4  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Formulas
I honestly don't understand this fetish people have for terminating decimal numbers. What's so special about them? Quote:
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 basephi, 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.  
September 19th, 2012, 04:42 PM  #5 
Newbie Joined: Sep 2012 Posts: 4 Thanks: 0  Re: Formulas
That's okay, I understand...

September 19th, 2012, 06:01 PM  #6  
Senior Member Joined: Aug 2012 Posts: 2,409 Thanks: 753  Re: Formulas Quote:
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.  
September 19th, 2012, 10:43 PM  #7 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Formulas
Maschke captured what I meant much better than I did.

September 20th, 2012, 07:43 AM  #8 
Newbie Joined: Sep 2012 Posts: 4 Thanks: 0  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.

September 20th, 2012, 11:26 AM  #9 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Formulas
I don't understand what you're asking, sorry.

September 21st, 2012, 04:10 PM  #10  
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Formulas Quote:
As others have pointed out, math and physics are not the same thing but the speed of light is a very poor example! Quote:
 

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