COGS 200 Lecture Notes - Lecture 1: Long Division

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The set of inputs for which a function is defined is its domain. The set of outputs that the function can give is its range. If there"s only on input that gets you to any given output, then the function is one-to one. If we have a well-formed question we can define a function, taking putative answers to that question as input, and giving yes" or no" as output. If we have a question/answer pair, we can define a function that gives true" or false" as output, depending on whether the second member of the pair satisfies the first. [turing and church"s] results entail something remarkable, namely that a standard digital computer, given only the right program, a large enough memory and sufficient time, can compute any rule-governed input-output function. That is, it can display any systematic pattern of responses to the environment whatsoever. (churchland and churchland, 1990)

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