Mohsen Ravanbakhsh wrote:
> Mathematics is just assuming some axioms and rules of inference and then 
> proving theorems that follow from those.  There's no restriction except 
> that it should be consistent, i.e. not every statement should be a 
> theorem.  So you can regard a game of chess as a mathematical theorem or 
> even a Sherlock Holmes story.  You may suppose these things "exist" in 
> some sense, but clearly they don't exist in the same sense as your 
> computer.
> Now I got it.
> Only under the* *assumption that space has a Euclidean metric (/You are 
> assuming the same to oppose/)- which is begging the question.  From the 
> operational viewpoint (There are other viewpoints as you know), 

Yes, but if they are not operational it is not clear how they relate to our 
world of experience.  Generally they are taken to be idealized models.

> measurements yield integers (in some units (If you want to keep the same 
> unit for two measurements as I said you'd encounter the irrational 
> numbers)).  

No.  For example the most accurate measurement to confirm Pythogora's theorem 
now possible would be to use ultraviolet light and count the number of 
wavelengths along each side and the diagonal.  Those counts would all be 
integers.  At present this is a practical experimental limit and so one can 
imagine using shorter wavelengths and making more accurate measurements - which 
will still come out as integers.  But according to current theories of general 
relativity and quantum mechanics there is also a limit to how short the wave 
length can be; an in-principle limit.  Measurements never yield numbers that 
are not integers (or ratios of integers).

Brent Meeker

>Real numbers are introduced in the Platonic realm to insure 
> that some integer equations have solutions(At least sometimes those 
> equations have some real counterparts).  Similarly imaginary numbers are 
> introduced to complete the algebra.  They are all our inventions - 
> except some people think the integers are not.
> You're right to some extends, but my point still is a point!
> Mohsen Ravanbakhsh.
> > 

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