System is in safe state if there exists a safe sequence of all processes.

Sequence $$[P_1, P_2 …P_n]$$ is safe, if for each $$P_i$$ the resources that can still request can be satisfied by $$P_i$$ currently available resources + resources held by $$P_j$$ with $$j \lt i$$

The above is from a presentation distributed by my OS II teacher. Assuming it is true, then doesn't this mean that the system is always in a safe state?

I conjecture that $$\forall$$ set of processes $$X = [P_1 ... P_n]$$ requesting for a set of resources $$[R_1 ... R_n]$$ $$\exists$$ a safe sequence $$S = \{P_i ... P_k\}, S: S$$ is a permutation of $$X$$.

Reasoning behind my conjecture. Suppose I had $$n$$ processes and $$1$$ resource(each process requesting it.) I could order these processes in order of priority, or ascending order of size and run them. If resources were increased to $$k$$, there will still be a sequence such that every process completes in finite time. The challenge merely finding it.

Am I wrong?