Also, an irrational exponent is the product of component factors.
b = Prod(0,inf) a^[x_i * 10^(-i)] = a^x
So even with irrational numbers, operations can be decomposed - such as exponentiation into multiplication of integer exponents and roots.
Which makes sense, because in the sequence definition of reals you need a way to generate the resulting sequence from the two original sequences.
I think you’re trying to claim more than is true.
Also, an irrational exponent is the product of component factors.
b = Prod(0,inf) a^[x_i * 10^(-i)] = a^x
So even with irrational numbers, operations can be decomposed - such as exponentiation into multiplication of integer exponents and roots.
Which makes sense, because in the sequence definition of reals you need a way to generate the resulting sequence from the two original sequences.
I think you’re trying to claim more than is true.