Not only have you turned into a waste of time and a waste of space on this forum, but worst of all, you try to belittle people. And you want to teach?! Yikes!!!
Actually, I do teach, and I teach very well. More importantly, most of my students want to learn and know how to learn. They study concepts in the order I present them because I know the material, and I know which topics build on others and are important to understand. The ones that don't do that will often fail. If they don't do well because they lack a foundation of understanding, I tell them that. I'll tell them if they don't master the earlier material, they will probably fail. It might seem blunt, but it's really important to address gaps in understanding, especially if later topics depend on those ideas. I'll often put in extra work with a student who has gaps in their knowledge, and filling in those gaps usually helps them significantly. The ones that put in the effort rarely fail.
At this point, a minimum of four people have tried to help you with this, multiple times each. I'm being blunt here too because it has become abundantly clear by now that you have significant gaps in your knowledge. Basic set operations, bijections, the natural numbers, infinity, etc, are all issues you have difficulty with. Pointing that out is not belittling you. Missing some prerequisite knowledge is not a flaw and I will never tell anyone that they
can't learn something. Everyone I have ever met is smart enough to learn this material and so are you. However, in preparation, you might need to learn more basic stuff first. If you don't fully understand the basics of the subject you are studying, you will probably fail. It's just as true for you as it is for my students.
Maybe saying that means I'm being a jerk. If I am, it's because being a jerk can sometimes be a pedagogically sound way to get someone to reevaluate the way they are approaching their studies. So, let me ask again: Take a step back and consider which situation is more likely - that you have destroyed a hundred-year-old piece of seminal mathematics or that you are lacking some understanding on the topic. Consider the fact that common responses to your posts in this thread are some variation of "I don't understand what you mean" or "Which part don't you understand?" and keep in mind that these are people who understand the topic and are trying to explain it to you. Think about how many explanations of the same idea have been written in the past 90 posts that had little to no effect.
Understanding is hard work, and sometimes you need take the time to work on things that you would rather skip. You need to work on them because they are necessary to accomplish the goal of learning the object of your main focus. Maybe you've skipped ahead too far. Maybe you need to learn to crawl before you can run. Maybe I'm full of shit. You're the only one who can decide. In any case, is this thread accomplishing what you wanted it to?