The document presents a mathematical result indicating that if d(n) is asymptotically smaller than f(n) and e(n) is asymptotically smaller than g(n), it does not imply that the product d(n)e(n) is asymptotically smaller than the product f(n)g(n). This challenges common assumptions in asymptotic analysis. The result is significant for understanding the behavior of combined functions.

1. R-4.17 Show that if d ( n ) is O ( f ( n )) and e ( n ) is O ( g ( n )) , then d ( n ) e ( n ) is not
necessarily O ( f ( n ) g ( n )) .