Artur Grzesiak
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#13 Any chances the video will be available?
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Thank you very much for these videos, highly appreciated.
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Puzzle. How many partitions does the empty set have, and what are they? There is one partition of the empty set, and it is the empty set itself. Checking from definition: Definition. A partition of a set \(X\) is a set \(P \subseteq P(X)\) such t…
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On Puzzle 32 It seems that they define partition as a pair of some set P and family of sets indexed by P satisfying some conditions. The set P is not defined uniquely. A partition with n parts may be defined by any set of cardinatlity n, whereas an…
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#11. A small typo instead of: ...and, for each \(p \in A\)... the book says: ...and, for each \(p \in P\)... .
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Re puzzle 32 There is a difference in defining symmetry. In the lecture: for all \(x,y \in X\), \(x \sim y\) implies \(y \sim x.\) In the book (definition 1.8): \(a \sim b\) iff \(b \sim a\), for all \(a,b \in A\) Implication is weaker than …
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Re puzzle 33 Every equivalence relation is reflexive and transitive by definition and these two properties define a preorder. Being symmetric is a further constraint, but it does not affect neither reflexivity nor transitivity (no idea how to proof…
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I find the course and community very inspiring and would like to say thank you for this rare opportunity. The material is extremely interesting. But to be honest I find a bit hard / overwhelming to participate actively and even follow all discussion…
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hey Evgenii - small side note on trinitarianism: prof. Harper is going to participate in this course.
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Enon, that is so cool. I know very little about GA, but it seems deeply fascinating, elegant and powerful. I would love to know more about it. https://github.com/enkimute/ganja.js maybe of some interest for you. The demos of this library are kind …
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:) - css is just pure insanity
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Actually I was allured to Rx from very pragmatic reasons and was totally unaware of the theory behind it. When writing Rx code I think about composing processes, but do not actively translate it to category theory as such. Still see a lot of paralle…
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Puzzle 4. List some interesting and important examples of posets that haven't already been listed in other comments in this thread. A very simple example. Let \(P = \{ (a,b): a < b \land (a,b) \in \mathbb{R^2} \}\) then following relations …
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Preorder relation is reflexive and transitive only, whereas partial order is anti-symmetric as well. In case of preorder if you follow arrows you may come back to your starting point, but in case of partial order you can only go in one direction (ap…