algorithm - Comparing the Bounds of Functions -
i understand general idea of bounds of functions; example, if function ƒ1(n) ∈ ω(n^2) then know ƒ1(n) element within constraints of lower bound n^2 , meaning ƒ1(n) can function grows slower or equal of n^2 . now start confused when talk other functions in regards bounds of ƒ1(n) . example, have statement claims this: if ƒ1(n) ∈ ω(n^2) and ƒ2(n) ∈ θ(n) then ƒ2(n) ∈ o(ƒ1(n)) i have hard time telling whether or not it's true or false. have 2 different approaches contradict each other: true - since ƒ2 tightly bound under n , can considered element within constraints of o(ƒ1(n)) because ƒ2 not grow slower ƒ1 . false - since ƒ1 has lower bound of n^2 , function ƒ2 , tightly bound under n , cannot considered element of upper bounds of ƒ1 since know ƒ1 not have upper bound grows slower n^2 . both of these approaches i've thought of seem valid me; think i'm getting confused on whether or not care lower bounds of
