C(n+1,k) = C(n,k-1) + C(n,k)
I don't get it

C(n+1,k) is the number of k-element subsets that can be formed from a set with n+1 elements i.e. {0,1,2,3,4,...,n}

C(n,k-1) is the number of (k-1)-element subsets that can be formed from a set with n elements i.e. {0,1,2,3,4,...,n-1} or {1,2,3,4,...,n}

C(n,k) is the number of k-element subsets that can be formed from a set with n elements i.e. {0,1,2,3,4,...,n-1} or {1,2,3,4,...,n}

I don't get how they are equal..