Why must time be treated as discrete in the mathematical model of a neural net?

In the mathematical model of a neural net, time is treated as discrete because the automaton is defined as a system that computes logical statements through reproducible responses to stimuli. To model these responses, the history of stimulation for an automaton with $n$ input neurons is recorded as a sequence of $n$-tuples of binary digits at specific moments in time.1

This abstraction allows the machine's behavior to be represented as a listing of responses to all possible stimuli, where a response is defined as a configuration of binary digits at a specified future time $t$. By treating time as discrete, the model can categorize stimuli as collections of individual histories, enabling the mathematical investigation of the machine's structure and its logical operations. This approach mirrors the foundational principles of the Turing machine, which also utilizes discrete time and a finite set of states to perform logical functions, allowing for the formal study of computability independent of the physical components used to build the machine.12