Little-O Times Big-O is Little-O
Jump to navigation
Jump to search
Theorem
Sequences
Let $\sequence {a_n}, \sequence {b_n}, \sequence {c_n}, \sequence {d_n}$ be sequences of real or complex numbers.
Let:
- $a_n = \map \OO {b_n}$
- $c_n = \map {\mathcal o} {d_n}$
where:
- $\OO$ denotes big-$\OO$ notation
- $\mathcal o$ denotes little-$\mathcal o$ notation.
Then:
- $a_n c_n = \map {\mathcal o} {b_n d_n}$