I'll be giving a small talk to the graduate students of my university on the topic of "counter-examples" and my first counter-example is Russell's paradox. I want to put the theorem in context, but admitedly, I have no idea what I'm talking about when it comes to logic and set theory. I want to know if what I wrote is not too much nonsense. I first cite the definition of set given by Cantor: "By a "set" we mean any collection M into a whole of definite, distinct objects m (which are called the "elements" of M) of our perception or of our thought." Then I say that this vague definition leads to paradoxes and presents Russell's paradox. Then I say that it is paradoxes of this kind that led mathematicians to look for an axiomatic theory of sets. I say that the commonly used set theory today is that of Zermelo and Fraenkel, in which the problematic "set" in Russell's paradox is not one in the ZF theory. However, I add, according to the works of Gödel, it is impossible to determine if the ZF set theory is or is not free of pardoxes. Given that what I wrote is not wrong, do you have suggestions for improvements or things I could add? Thanks!