What I would like to share with you today is my impression of how Mathematics is built and how it works internally. I believe this is an important thing to know about, because, over the course of my early studies, I have met with far too many people who have expressed their interest in Mathematics at first, but literally ran away later on. Why? Well, because they were terribly unaware of how it works at all! We all know that kind of people – their favorite line is “There are no numbers and too many letters, this is no math!”.
Nowadays, having an idea about set theory is an absolute must for everyone who is considering looking into higher level Mathematics. This is mostly because of how the modern Mathematics is built – it is no longer about putting random thoughts together and formulating observations based on our intuition. Rather, it is formalized, in the strict sense of the word.