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In my algebra book matrices operations looks like a kind of "algorithm". How do matrices operations are defined under ZFC ? Are they applications ? Are they Turing machine ? Are they something else ?

toto
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  • Look up recursive sets. The μ-recursive functions is exactly the ones computable by a turing machine. – Mano Plizzi Jun 13 '17 at 10:24
  • How Turing machines are defined by sets can be read over here. But I know (from the other thread) that you actually want to know how this definition gives rise to the function defined by the Turing machine (formally as map in ZFC), a.k.a. the corresponding algorithm, right? Maybe you should include this in the question, the first close vote is dropped for being "too broad". – M. Winter Jun 13 '17 at 10:24
  • Yes, but since i'm french, that is kinda hard for me to express fluently and efficiently ! – toto Jun 13 '17 at 10:29
  • the edit made this so much less clear. Are you asking how natural numbers are defined in ZFC ? – mercio Jun 13 '17 at 10:32
  • @mercio toto an me had a discussion over here. Below my answer the discussion drifted away from the topic. He asked how the concept of algorithm can be implemented in ZFC. He initially wanted to know how this can be done to define matrix multiplication because he only knows about Turing machines, but does not know how they and their defined partial functions emerge in ZFC. – M. Winter Jun 13 '17 at 10:38
  • Hope it makes it more clear, sorry for my bad english – toto Jun 13 '17 at 10:44
  • In you previous post you asked (and received an answer) about "what are matrices": they are maps, i.e. functions, i.e. sets. What is an "operation" on matrices ? A function from matrices to matrices or numbers (e.g. the determinant). – Mauro ALLEGRANZA Jun 13 '17 at 11:28
  • But, in my algebra book, the "operation" is a kind of algorithm, and it disturb me, since i don't know if an application can act this way. I mean like an algorithm. – toto Jun 13 '17 at 11:31
  • @toto You should really rephrase your question and try to reopen it. If you have problems with the language, then take time or ask for help. For example, it is possible to write a question in another language than english and ask for a translation. To the topic: As I said, algorithms as defined by Turing machines are specially defined (partial) functions. If you want to know how this is done exactly than this should be the main point of your question. Refering to matrix operations etc. will just distract and lead to close votes because it seems like a duplicate. – M. Winter Jun 13 '17 at 12:35

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