In the book Introduction to artificial intelligence Ertel asks this question (exercise 1.5(a)):
Why is a deterministic agent with memory not a function from the set of all inputs to the set of all outputs, in the mathematical sense?
I don't even know why this statement would be true! I mean, I understand that mathematical functions are "pure functions" and thus do not have "side effects." An agent with memory can be viewed as a function with side effects and thus can't be a pure math function. But what prevents from choosing as the set of all inputs the "spacetime" of input? Doing so brings back the agent with memory to a pure function which can be represented as a mathematical functions!
Am I missing something or is what I say correct?