Matthew asked:

> Is there a closed monoidal partial order which does not have arbitrary joins?

How about \\(( [0,\infty), \ge, +, 0)\\)? Just remove the initial/bottom element from \\(\textbf{Cost}\\). Does that work?

Ooops, that's a meet not a join.

How about \\(( (-\infty,\infty), \ge, +, 0)\\)?