Determine if the given set of whole numbers is closed under addition. \( \{4\} \) Closed Not closed

The set \( \{4\} \) is indeed closed under addition because when you add any number in the set (and there's only one, 4) to itself, the result is still 4. So, \( 4 + 4 = 8 \) is not in the set which shows that while merging and collecting it still sticks to itself in totality. However, let’s think about how closure works with more diverse sets. A more complex set like \( \{3, 5\} \) would not be closed under addition since \( 3 + 5 = 8 \) falls outside the original set. Think about composing numbers together; the magic happens when they all harmoniously dance within their own group!