How Integers Behave

Integers are closed under addition, subtraction, and multiplication: combine any two with those operations and you always land on another integer. 7 − 12 = −5; (−6) × 4 = −24. You never fall off the set.

Division is the exception — 7 ÷ 2 = 3.5 escapes into fractions, so integers are not closed under it.

They also split cleanly into even and odd, alternating along the line in both directions: ...−2, −1, 0, 1, 2... with even and odd taking turns.