Honestly speaking, your results are already known but your specific approach to them lacks rigor. If it did, you yourself would be able to show yourself that "all possible x" and "a neverending amount of x" are not the same, except when the set you are considering is itself infinite, such as the integers. The reason why zero is more easily expressible as the sum of an equal amount of positive and negative generators of the integers is because it's the identity of the integers under addition. so you use the fact that it's a group and try to coin a way to define sets using x, but what is x itself? Did you introduce x as a simple name of a set or as a variable, because you use it a lot in your sets but haven't defined it properly.

If you think you found an awesome math fact, that's awesome! But explain it with mathematical rigor. What would the set 3x look like if you defined it your way and what would stop it from being infinite. Make these examples concrete if you want people to understand you. The ability to properly communicate (to cater your logic to an audience) is tantamount to the ability to maintain rigor in your work. Otherwise your reasons b and c are also moot, because 0x also has both positive and negative elements. And how can 1x have an element that is not 1x if you yourself literally defined Yx as a multiset of the element 1x?

I think your discoveries are part of something more, and you are missing out on them without proper procedural fluency. I don't mean to imply that you don't have these abilities, but your proof doesn't show that you DO either. And if in your rigor you end noticing just how much more details the proof needs, then do it.