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				My favourite description of a computer is a function
 
 f(p, in) -> [out]
 
 such that for any other function g a value of p can be found such that
 
 f(p, in) = g(in)
 
 If a machine can be transformed into a function f that has this quality, it is a computer.
 
 Edit: obviously g has to be computable so the actual rule is a bit different, but the gist of it is this.
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