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Category: Formalized math

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Formalized math

The math book rewritten with implicit arguments

By Victor Porton
On May 20, 2017

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…

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Formalized math

How proof by contradiction differs of direct proof

By Victor Porton
On February 26, 2014

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,…

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#math logic#mathematical logic#proof by contradiction
Algebraic general topology Category theory Formalized math General Topology

New definitions of products and coproducts in certain categories

By Victor Porton
On September 27, 2013

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…

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Formalized math

Toward formalization of partial infima and suprema

By Victor Porton
On December 31, 2012

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.

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  • SCIENCE
  • Home
  • Algebraic General Topology
  • Axiomatic Theory of Formulas
  • Limit of a Discontinuous Function
  • More
  • Prize
  • SCIENCE
  • Home
    • Blog
    • Soft
  • Algebraic General Topology
    • Paperback
    • Ebook
    • PDF
  • Axiomatic Theory of Formulas
    • Paperback
    • Ebook
    • PDF
  • Limit of a Discontinuous Function
  • More
    • Donate
    • Review
    • Publish
    • Politics
  • Prize