yes, thank you, i see. Apparantly the positive real numbers are a vector space according to the operations defined in the OP
Another question... ++ is regular multiplication, ** is regular exponentiation
we don't have to worry about the 'object' 0 being in V since no positive base to a real number exponent can give 0.
I don't know what to call 0... a vector?... a scalar? both?
Are not the elements of V bases? The elements of R exponents?
That would mean the bases are vectors the exponents scalars?
is this correct?
That depends. For example, if you consider the "object" as belonging to , it is a vector, and satisfies for all , so is the zero vector. If you consider the "object" as belonging , it is a scalar and satisfies , so is the identity element for the product of scalars.
On the other hand, the "object" does not belong to but belongs to so, necessarily is an scalar, satisfying for all so, is the identity element for the sum of scalars.