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rakhim.org | ||
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math.andrej.com
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| | | | | [AI summary] The discussion revolves around the nuances of proof methods in constructive mathematics, particularly the distinction between proof by contradiction and proof by negation. Key points include the definition of irrational numbers without relying on the law of excluded middle, the use of contrapositive in proofs, and the limitations of certain classical theorems like the intermediate value theorem in constructive settings. The conversation also touches on the philosophical and practical implications of these proof methods in both classical and intuitionistic logic, as well as the role of type theory and univalent foundations in modern mathematical proofs. | |
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www.jeremykun.com
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| | | | | Previously in this series we've seen the definition of a category and a bunch of examples, basic properties of morphisms, and a first look at how to represent categories as types in ML. In this post we'll expand these ideas and introduce the notion of a universal property. We'll see examples from mathematics and write some programs which simultaneously prove certain objects have universal properties and construct the morphisms involved. | |
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aeon.co
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| | | | | Some have thought that logic will one day be completed and all its problems solved. Now we know it is an endless task | |
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dehora.net
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| | | Back in 2013, I started a series of posts on programming languages I found interesting. One of the languages I wanted to write about at that time was Rust. As often happens, life got in the way, and it's only now that I'm coming round to a long overdue post. This is one of a series of posts on programming languages and you can read more about thathere. | ||
