To add to this, another mathematical term to be familiar with is "isomorphism". It quite literally means showing that two structures are the same, and perserve the same binary relations (coming from modern Algebra).

If you can show that domain A is isomorphic to domain B, then all of the things you know how to do for domain A can be trivially applied to domain B. Thinking about solving problems in terms of isomorphisms has been tremendously helpful for my day-to-day problem solving.