I've found this demonstration (for this problem taken from "Mathematical methods of Classical Mechanics" by V. I. Arnol'd), and I could not decode this particular step:
A $k$-dimensional plane can be uniquely identified by the value of its symplectic form. The symplectic form takes values in the intervals $[0,k]$
And so:
there is a total of $[k+1]$ different symplectic forms for a k-dimensional plane in $\mathbb R^{2n}$.
What does the first sentence mean? Couldn't 2-forms be of whatever value?