Definition 2 (Large Language Model). Let S be a computable seta of all the finite-length strings of alphabet A and (s0, s1, . . .) be an one-to-one enumeration

Definition 2 (Large Language Model). Let S be a computable seta of all the finite-length strings of alphabet A and (s0, s1, . . .) be an one-to-one enumeration of all the elements in S. A large language model, denoted h, is a function that completes the input string s ∈ S using the function’s predicted tokens h(s), in a finite time. Function h is attained procedurally using a set of training samples of input-completion pairs. For an arbtrarily large duration and an arbitrarily small error with respect to any definition of error you choose, there exists an LLM in the above sense which models the dynamics of your brain with that small error.