The problem is that you can define all you want, but then you need to figure out what you can do with that number. For example, if j is the solution of 1/x = 0, what would be the solution of 2/x = 0? What are the properties of j?
Of course you can make this a bit clearer and instead of the name "j" you use the name "error", with the understanding that error + x = error - x = error * x = error / x = x - error = x / error = error, whatever real or complex number x is. That's just not very useful. And then you run into trouble when a correct calculation shows you for example that the solutions to a problem are all values x that solve x^2 = 1 or 1/x = 0. So instead of two solutions +1, -1 you suddenly have three solutions +1, -1 and error, which is quite rubbish.
Or, the answer in short: We don't do this because it is a rubbish idea that is in no way helpful.