I have a question regarding optimal mistake bound for learning algorithm
There is a famous fact that $VC(C) \leq Opt(C)$,
where $C$ - set of learning concepts,
VC(C) - VC dimension of C,
$Opt(C)$ - the smallest mistake bound (of the best learning algorithm) on the hardest learning concept $c \in C$ .
I don't understand why $VC(C) \leq Opt(C)$, in my opinion the notion of best algorithm $A$ is so vague that you cannot for sure say that $VC(C)$ is not more than $Opt(C)$
For example, $VC(line\ on\ the\ plane)$=3 , it means that $Opt(C) \geq 3$ in words it means for the hardest concept $c \in C$ (represented as a line on the plane) the number of mistakes of the best learning algorithm is more than 3.
Why the above fact is so strong?