The math book rewritten with implicit arguments
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 on this topic, learn what is called “dependent lambda calculus”. (Sadly, I do […]
How proof by contradiction differs of direct proof
This 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, people, are capable of doing irrational things and to be discouraged. I wrote […]
New definitions of products and coproducts in certain categories
I 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 certain category (“category of continuous morphisms”) having endomorphisms of the aforementioned category as […]
Toward formalization of partial infima and suprema
I’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.