I am changing my research field
I failed to make progress in research of product of funcoids, the next thing I should research in my research plan. I also fail to solve any of my open problems. Thus my research is stalled. I hope other people can solve the problems I formulated. Due this crisis I decide to change my research […]
Untyped formalized systems are wrong
First, I’m not (yet) an expert in formalized mathematics. I know Isabelle/ZF better, but have only overall view of Isabelle/HOL. Nevertheless I want to tell my opinion on typed (such as HOL) vs. untyped (such as Isabelle/ZF) systems. Slawomir Kolodynski converted me into his religion of doing formalized math with Isabelle/ZF and answering “yes” to […]
My motivation to do math research
In the past I considered my purpose to exactly and directly follow commandments of Bible. I had some purposes hardly set as the aim of my life. My life was driven by these purposes not by my wish or my heart. I understood that it was wrong, Bible is more subtle than just a list […]
Restricting a reloid to a trivial atomic filter object
I proved the following (not very hard) theorem: Theorem $latex f|^{\mathsf{RLD}}_{\{ \alpha \}} = \{ \alpha \} \times^{\mathsf{RLD}} \mathrm{im} \left( f|^{\mathsf{RLD}}_{\{ \alpha \}} \right)$ for every reloid $latex f$ and $latex \alpha \in \mho$. See the online article about funcoids and reloids.
My math sickness
I’m sick with the following: I repeatedly formulate conjectures which have trivial counterexamples and am stuck attempting to prove these true not seeing counterexamples. I should less rely on my ideas what is a true conjecture. I just need to become humbler and less proud. Hopefully now I have enough counter-examples for me to follow […]
“Filters on Posets and Generalizations” – updated
Filters on Posets and Generalizations online article updated as an accomplishment of this plan. This is important primarily to extend the category of pointfree funcoids with objects being arbitrary posets (even without least element). That way this category would become more “complete”. To extend that is required a definition of intersecting elements of a poset […]
Generalization in ZF
I wrote short article “Generalization in ZF” accompanied with Isabelle/ZF sources. This is a draft and alpha. I await your comments on both the article and Isabelle sources. I’m sure my Isabelle sources may be substantially improved (and I plan to work over this). Comments are welcome. After hearing your comments and improving the files, […]
A little error corrected
I corrected a small error in “Filters on Posets and Generalizations” article. The error was in Appendix B in the proof of the theorem stating $latex (t;x)\not\in S$ (I messed $latex t$ and $latex \{t\}$.)
I take a vacation in my research work
I decided to dedicate my free (of working as a programmer) time to write a book about religion (What book? It will be a surprise.) So in a few nearby months I am going to not continue my math research. I am going to return to math research after I will finish that religious book. […]
Strong vs weak partitioning – counterexample
My problem whether weak partitioning and strong partitioning of a complete lattice are the same was solved by counter-example by François G. Dorais. Remains open whether strong and weak partitioning of a filter object is the same.