I am looking for pedagogically motivated examples (like elementary proofs,or simple problems) of "abstraction in action" ? I am looking for good specific examples (pre-university level or first year undergraduate level ) that could very clearly address the following questions
- When did the abstraction occur?
- What prompted the particular abstraction?
- What or which property was abstracted?
- Why was the abstraction necessary? I mean how the abstraction was necessary to continue further?
- What could have been other possible abstractions but they were rejected because they couldn't have been very useful to continue further.
Essentially,my question is an attempt to "show few examples (like elementary proofs,or simple problems) which appear rich in abstractions when observed through the lens of abstraction?"