algorithm - Comparing the Bounds of Functions -
i understand general idea of bounds of functions; example, if function Æ’1(n) ∈ ω(n^2) then know Æ’1(n) element within constraints of lower bound n^2 , meaning Æ’1(n) can function grows slower or equal of n^2 . now start confused when talk other functions in regards bounds of Æ’1(n) . example, have statement claims this: if Æ’1(n) ∈ ω(n^2) and Æ’2(n) ∈ θ(n) then Æ’2(n) ∈ o(Æ’1(n)) i have hard time telling whether or not it's true or false. have 2 different approaches contradict each other: true - since Æ’2 tightly bound under n , can considered element within constraints of o(Æ’1(n)) because Æ’2 not grow slower Æ’1 . false - since Æ’1 has lower bound of n^2 , function Æ’2 , tightly bound under n , cannot considered element of upper bounds of Æ’1 since know Æ’1 not have upper bound grows slower n^2 . both of these ap...
