Disprove Big-Oh ---Week 10

last week, we introduce the big-Oh prove, this week we disprove the big-Oh.
Here is one of the examples:

Disprove n^3  O(3n^2)

we first negate  cR+,  BN, nN, n>=B, n^3<=c(3n^2)

  cR+,  BN, nN, n>=B^( n^3)>c(3n^2)


proof:

assume c belongs to R+ and B belongs to N, (Generic c,B)
       pick n=B+ceil(3c)+1  (then n belongs to N)
       then n>=b
     
       then n>=B
       then n^3=n*n^2
       then n^3>3c*n^2 (since n>3c)
       then (n>=B)^ n^3>3cn^2

then  cR+,  BN, nN, n>=B^( n^3)>c(3n^2)