*Why?  "Mathematical" means nothing but not self-contradictory.  Sherlock
Holmes stories are mathematical.  That doesn't mean Sherlock Holmes exists
in some Platonic realm.
*

Brent,

What do you mean by that? I do not get your point.
Anyway I do not insist that it should be realizable. But I have examples in
which we need them!
Consider the use of Pythagoras theorem in nature. There are many cases in
which the distance between two points should be irrational.

-- 
Mohsen Ravanbakhsh,

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