I want to know the answer to the following question:
What permits elements with different mathematical starting points to be taken care of in a flexible manner while holding their key basic aspects?
All the background I'm provided with is that "One of the most familiar examples of a group is the set of integers together with the addition operation, but the abstract formalization of the group axioms, detached as it is from the concrete nature of any particular group and its operation, applies much more widely.". Is that enough to answer the question?
Answer: yes