Algorithms aren’t necessarily finite, eg “while True, print 1”. Also, an irrational exponent is the product of component factors. b = Prod(0,inf) a^[x_i * 10^

Algorithms aren’t necessarily finite, eg “while True, print 1”. 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.