[FOM] Closure under addition

Arnon Avron aa at tau.ac.il
Wed Dec 15 01:39:43 EST 2004

On Mon, 13 Dec 2004, Vladimir Sazonov wrote:

> It seems reasonable to assert that our Real World is closed at most
> under addition (if closed at all - this is an idealization), but not
> under multiplication. The latter leads very easily to physically
> not existent exponential computations (2*2*2*...*2 = 2^1000 =
> practical infinity). This leads to the conclusion that multiplication
> and exponential are only partial functions, although computable.

It is beyond me how is it possible for our Real World to be closed
under addition and not under multiplication or even exponentiation.
Thus 2^1000 is the output of the following simple program that 
need only closure under addition:

   n:=0 x:=1
   Until n:=1000 do x:= x+x n:=n+1 od

What can the meaning of "closure under addition" possibly be if
the above program (requiring just 2000 additions) is not executable
(according to Sazonov)?

Arnon Avron

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