Can we have a strictly monotonically increasing/decreasing sequence generated by a distributed system?

Question

Just what the title says. Can we have a strictly monotonically increasing/decreasing sequence generated by a distributed system (without a single point of failure)?

My current thoughts are that this is a consensus problem, and is thus impossible to achieve in an asynchronous messaging system (like the Internet). Another way I look at it is that if we could generate such a sequence in a distributed system, then the problem of total ordering is solved.

Please correct me if I'm wrong.