Thank you for the input, I’m an engineer and phd student in engineering so I based a lot of this on intuition, there’s an order gap for me to write something tr

Thank you for the input, I’m an engineer and phd student in engineering so I based a lot of this on intuition, there’s an order gap for me to write something traditionally axiomatic and rigorous, but my understanding is that algebra is based on logic and problems in general, and I would like to know any logical fallacies at the very least. Thank you for reading it.