I have rewritten my math book (volume 1) with implicit arguments (that is I sometimes write $latex \bot$ instead of $latex \bot^{\mathfrak{A}}$ to denote the least element of the lattice $latex \mathfrak{A}$). It considerably simplifies the formulas. If you want to be…

read moreThis my post is about mathematical logic, but first I will explain the story about people who asked or answer this question. A famous mathematician Timoty Gowers asked this question: What is the difference between direct proofs and proofs by contradiction. We,…

read moreI have updated this article. It now contains a definition of product and coproduct for arbitrary morphisms of a dagger category every of Hom-sets of which is a complete lattice. Under certain conditions these products and coproducts are categorical (co)products for a…

read moreI’ve written a short note about suprema and infima in formal math: Toward formalization of partial infima and suprema It is especially useful for these who do math formally (in proof assistants), but may be inspiring for regular mathematicians too.

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