Again, wrong. You're (purposely?) mixing up redefinition of results vs the redefinition of algebra. Redefining the algebra behind division (and all other basic operations in the process) is a valid approach to tackle the division by zero problem. Redefining its result alone is not. And, incidentally, none of those two will do you any good with IEEE numbers.
You simply can't just say " x / 0 = 42 " without redefining division, substraction and multiplication. And all other operations in the process.
division by zero is sometimes undefined, but there is no natural reason for it to give an error. For example, IEEE defines floating point division by zero as infinity, whereas dividing an integer by zero is defined as an error.
The example is wrong since IEEE does not define division by zero as infinite to be a valid result. And, under the algebra rules used by IEEE floats there IS a very good reason for it to give an error. This is not a philosophical discussion; you don't need to sit down with a Fields medal mathematicians in order to understand why the above statement is incorrect.