>>11638371Firstly, you are an idiot. Neither limits nor rings are required to show a contradiction. Thinking limits have anything to do with this means that you not only failed your algebra class but also your analysis class.
Secondly, you should learn how to properly articulate your arguments. This includes logical operators and LaTeX for presentation. This is a fucking chinese cartoon imageboard, I am not deciphering child's scribbles.
Thirdly, division is defined through multiplication. A fraction a/b is defined as such an element of c that a=bc. If you take b equal to 0, then 0c should equal a for an arbitrary a. In other words, your algebraic structure collapses to a single element and you cannot introduce division by zero which is consistent with all existing addition and multiplication properties. Introducing it for a single element is pointless. You can give up some of the properties and define division by zero through compactification of your space. But you should finish school to learn about that, so see you in 6 years OP.