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# Scott Finnie

• @John Baez [#15]: thanks. Definition. A partition P1 is finer than P2 if: P1and P2 partition the same set, and Every part of P1 is a subset of some part of P2. Yes, that makes sense and is easier to read. I had an initial thought that sub…
• Thanks @Charles Clingen [#17], fixed. Glad you found it useful.
• Minor typo (I think) in your lecture John: But you can still try to give me a "best approximation" to the nonexistent natural number a with 2a=4. Think that should be 2a=3? If not, it's a "thinko" on my part (kudos to Patrick O'Neill for the …
• @Anindya #50: thanks.
• @Keith @Shaaz @Anindya: thanks for the question and explanations. Assuming I understand right then, this is just different terminology for the fundamental difference between a preorder and a poset. At least, using the common meaning for those thin…
• Another attempt to summarise things with pictures and informal description. This time: Partitions. Comments/suggests greatfully accepted as before. Partitions are covered in section 1.2.1 of the book. They're also covered in Exercise 3. What is…
• Adding my thanks too John: for your energy and patience as much as the simple understandability of your lectures & comments. The pace is at the upper end for me. I'm with Nathan in having limited time and being a slow reader of maths. I am, h…
• @John #44. Thanks for the explanation. Learning and enjoying!
• I found this statement in section 1.1.1 confusing: There is no operation on the booleans true,false that will always follow suit with the joining of systems: our observation is inherently lossy David Chudzicki's answer above helped: I gues…
• @John #40: thanks. I've updated the diagram accordingly, though a side effect is your post now shows the new version (apologies). You can use https://raw.githubusercontent.com/sfinnie/CategoryTheoryCourseNotes/6bbcc770474a8945ee4e47e273a65909f979b…
• @John #35 & #37: thanks. Have updated #33 to use "less than or equal to", which makes the description for preorders less clumsy. Great that you're open to alternative descriptions. I'll try to add as and when time allows.
• Posting this as someone who learns best from concrete examples and geometric representations, on the basis that trying to explain something is a good way to test one's understanding. If it's inappropriate for the forum please just say. I ask forbe…
• Chris Nolan #15: I was wondering that too, thanks for asking. Testing my understanding of the answers then: For any pair of objects \(x, y\) in the set of objects, exactly one of the following must hold: \(x\) is comparable to \(y\), or \(x\) is…
• As someone with limited time due to other commitments, just wanted to say I really appreciate the length and tone of the lectures John.
• Another question on the lossy nature of observation. Re-stating the final paragraph of section 1.1, from an information-theoretic perspective: Let the initial system \(X\) have information content \(Ix\) Subject \(X\) to a lossy observation \(f\)…
• Section 1.1 says observation is inherently lossy: in order to extract information from something, one must drop the details. Is that true of observation in general? Or does it conflate observation with the human approach to it - namely abstra…
• @Bob Haugen (51): Dataflow as a partially ordered set had also occurred to me (as long as it's an acyclic graph).