Thank you so much for your time and observations:
The general purpose of the post was to explain to the general public how the average mathematician thinks and makes research through very simple examples.
I never mention the ZF axiomatic system because I acknowledge that even as exciting as it is for me, or in general to any mathematician, it is not for my target reader.
I agree that I left some things in the air and I was very informal with my explanation. I could have defined with all the formality an operation, as what it is, as a function, and explain that when we say that an operation is well-defined, it's because it satisfies that definition. Though, I wanted to keep motivated the reader,and be as intuitive as possible...most of my followers don't even have an engineer level of math.
This post was't even tagged with #SteemSTEM, although I asked for your opinion because I intend to write divulgative articles, such as this, for your community: I really want to be part of it!
I definitely agree, however, that I missed the sources, both for the images and for further reading, as well as ti check if the images are of public domain.
I sincerely appreciate that you took the time, as a PhD math student, to read it and give me some suggestions for the near future. And I'm glad you liked it :)