Well, if you add nuance, it’s fine. The limit of a number divided by another number x as x approaches zero is infinity.
That’s almost the same thing.
Much of math just doesn’t work if you try to add infinity as just another number. You say dividing by zero is undefined because once you have that infinity anything further you do with it is also going to be infinity, it breaks the way you prove things, it breaks the idea of a number line.
There is plenty of math that deals with infinities, but it is all handled delicately.
That’s almost the same thing.
Much of math just doesn’t work if you try to add infinity as just another number. You say dividing by zero is undefined because once you have that infinity anything further you do with it is also going to be infinity, it breaks the way you prove things, it breaks the idea of a number line.
There is plenty of math that deals with infinities, but it is all handled delicately.