How Tricky the Most Basic Math Is. All the Assumptions in a = b

Equality-Level Assumptions (present in ANY equation, including )

1. A is a defined symbol

2. B is a defined symbol

3. A refers to a stable quantity

4. B refers to a stable quantity

5. A and B exist within a defined domain

6. A and B are comparable objects

7. The comparison is made under consistent conditions

8. The symbol “=” has a fixed meaning

9. Equality represents exact equivalence unless otherwise stated

10. A’s definition has not changed

11. B’s definition has not changed

12. Units of A and B are compatible

13. No hidden unit conversion exists

14. No coordinate transformation has been silently applied

15. No hidden scaling factor exists

16. A is not time-varying unless explicitly stated

17. B is not time-varying unless explicitly stated

18. Measurement of A is valid (if measured)

19. Derivation of B is valid (if derived)

20. Equality is not being forced by definition unless declared

21. Equality is not circular unless declared

22. Identity is well-defined

23. Reflexivity holds

24. Symmetry holds

25. Transitivity holds

26. Substitution is valid

27. Algebraic manipulation preserves equality

28. Domain rules are consistent

29. No contradictions exist in the system

30. The mapping from symbol → physical quantity is valid