Group theory
Commutative operators are common in our daily lives. For example, 7 · 3 is also the same as 3 · 7. However, not all operations are commutative. For example, 7÷3 is different from 3÷7 (and neither of these results is an integer), and 73 is different from 37. Therefore, not all combinations of number sets and mathematical operations can form an abelian group—or even a group at all.