Today I finally experienced the power of something I learned in university: propositional and predicate logic.

Many developers I know think that such education is useless. Well, today I have proven that it is very useful. On a day to day basis, working on banking software, complexity in purely logic is very low. However, we have a screen that must show or hide elements based on some input values and conditions associated with certain elements. How hard can that be, right? Well, there are many variables to take into account and as such it's absolutely not trivial.

This screen didn't work properly and maintaining the code is hard as there is a lot of logic to show/hide, enable/disable things and so on. After quite some time and attempts by fellow developers, I decided to refactor the whole thing. I'm responsible for the quality of the software and it was quite degrading, so I had to do something.

In order to get things working properly, I defined collections of constants (ui elements) and predicates. Then, I defined for which element what predicates must be true, in order to hide/show, disable/enable etc. I then translated these predicates into code. And guess what? It works! Of course it works. It's logic. But I'm very pleased I finally could actually use some of all the math I studied!

It should be possible to prove the collatz conjecture by mapping the unit digit transitions between numbers, namely into a finite state machine. From there we could use predicates and quanitifiers to prove, by process of exclusion, that for any given combination of 10s digit and 1s digit, no number can transition to anything but whats specified in the state machine assuming that number equals x in x3+1 or x/2

Ipso facto, a series of equations proving by process of elimination, that state machines transitions are the only allowable ones, would prove the collatz conjecture by proving the fsm is a valid representation for any given integer N.

I'm actually working on it now but I don't know enough about modular arithmetic and predicate logic to write a proof. I just have the state diagrams on some dot matrix paper at the moment.

If anyone wants to beat me to it, feel free.

So for example any number ending in 13, will, after x3+1, end in 40.

Any number ending in 40 will end in 20. Any number ending in 20 will end in 10, which will end in 5 as the unit digit.

It's easier to prove in the single digit case, and the finite state machine for that is already written, at least on paper.

I'll post pictures when I get a chance.