Math can, and in the case of QM, must use infinities and 0-dimensional particles which can not exist in reality.

I'm a little confused by this objection to say the least. Could you express your views on the following topics in mathematics, particularly when they are used for real world applications, whether it be physics, computer science or engineering?

1. The use of the "null vector" in linear algebra

2. Limits approaching 0 in calculus

3. Generalizing the rules of 3 dimensional space to represent 4 dimensional space

4. Complex numbers and their various applications, particularly if you think we shouldn't use the square root of negative one if it has no identifiable physical properties