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I agree completely. The only risk is that once you get to real analysis, your prof will yell at you for mixing notions of complexity and computability into your
by bigred100 7y ago
I agree completely. The only risk is that once you get to real analysis, your prof will yell at you for mixing notions of complexity and computability into your ideas of what a function is (happened to me).
- melvinroest 7y agoOf that sounds harsh. What do you mean by complexity? I understand computability (having made a Turing machine from a mostly XML based language :D).
- bigred100 7y agoA function is (at least formally) a relationship between two sets of things. It doesn’t matter whether there’s any sort of algorithm that lets you input an object from the domain and calculate the corresponding image under the function, or even an approximation. This came up when we were talking about Dedekind cuts or something like that so it’s very much not pedantry at all in that sort of context.
- lonelappde 7y agoThe main difference between pure math and computer science is that mathematicians assume uncountable sets exist and then use that to prove all sorts of nonsense that are not true in the physical or computable Universe.
- sedeki 7y agoGive an example of this kind of _nonsense_, please.
- blt 7y agoMany CS papers, at least in machine learning, state an algorithm in terms of real numbers and use results from real analysis to prove properties of the algorithm.
- chrisoverzero 7y agoGiven that Cantor’s Diagonal Argument – which demonstrates the existence of uncountable sets – is the technique which underlies Turing’s solution to the Entscheidungsproblem, you might want to re-examine your assumptions.