what does it mean that the bound $2n^2 = O(n^2)$ is asymptotically tight while $2n = O(n^2)$ is not? We use the o-notation to denote an upper bound that is not asymptotically tight.

The definitions of O-notation and o-notation are similar. The main difference is that in $f(n) = O(g(n))$, the bound $0 \leq f(n) \leq cg(n)$ holds for some constant $c>0$, but in $f(n) = o(g(n))$, the bound $0 \leq f(n) \leq cg(n)$ holds for all constants $c>0$. so what is the differnce in big-O notation and small-o notation  ?

What does it mean that the bound $2n^2 = O(n^2)$ is asymptotically tight while $2n = O(n^2)$ is not? We use the o-notation to denote an upper bound that is not asymptotically tight.

The definitions of O-notation and o-notation are similar. The main difference is that in $f(n) = O(g(n))$, the bound $0 \leq f(n) \leq cg(n)$ holds for some constant, $c>0$, but in $f(n) = o(g(n))$, the bound $0 \leq f(n) < cg(n)$ holds for all constants, $c>0$.

So what is the difference in big-O notation and small-o notation?

what does it mean that the bound $2n^2 = O(n^2)$ is asymptotically tight while $2n = O(n^2)$ is not?

The definitions of O-notation and o-notation are similar. The main difference is that in $f(n) = O(g(n))$, the bound $0 \leq f(n) \leq cg(n)$ holds for some constant $c>0$, but in $f(n) = o(g(n))$, the bound $0 \leq f(n) \leq cg(n)$ holds for all constants $c>0$.

what does it mean that the bound $2n^2 = O(n^2)$ is asymptotically tight while $2n = O(n^2)$ is not? We use the o-notation to denote an upper bound that is not asymptotically tight.

The definitions of O-notation and o-notation are similar. The main difference is that in $f(n) = O(g(n))$, the bound $0 \leq f(n) \leq cg(n)$ holds for some constant $c>0$, but in $f(n) = o(g(n))$, the bound $0 \leq f(n) \leq cg(n)$ holds for all constants $c>0$. so what is the differnce in big-O notation and small-o notation ?

what does it mean that the bound 2n^2 = O(n^2) is Asymptotically tight while 2n = O(n^2) is not?

The definitions of O-notation and o-notation are similar. The main difference is that in f(n) = O(g(n)), the bound 0 <= f(n) <= cg(n) holds for some constant c>0, but in f(n) = o(g(n)), the bound 0 <= f(n) < cg(n) holds for all constants c>0.

what does it mean that the bound $2n^2 = O(n^2)$ is asymptotically tight while $2n = O(n^2)$ is not?

The definitions of O-notation and o-notation are similar. The main difference is that in $f(n) = O(g(n))$, the bound $0 \leq f(n) \leq cg(n)$ holds for some constant $c>0$, but in $f(n) = o(g(n))$, the bound $0 \leq f(n) \leq cg(n)$ holds for all constants $c>0$.