 To get clearer on what is at issue here, let us introduce another notion, being “bounded from below” or “having a lower bound”. We can say that an order &lt; on a domain is bounded from below if any subset of that domain has a lower bound. More precisely, a lower bound of a given set is any element that is more minimal or equal to all of the elements of the set. For example, 1, 2, and 3 are all lower bounds of the interval [3, 4, 5]. A lower bound of a set does not need to be an element of the set itself. Consequently, the chain \(f &lt; \ldots d_{3} &lt; d_{2} &lt; d_{1}\), is bounded from below. More generally, any finite chain is set-theoretically well-founded and bounded from below. We’ve just seen that some infinitely descending chains of dependence may be bounded from below yet fail to be set-theoretically well-founded. As Rabin &amp; Rabern (2016: 360) put it, an infinitely descending chain may or may not have a “limit”, where limit is the greatest lower bound of a set. In the previous example, 3 is the greatest lower bound of the interval [3, 4, 5]. So, one might suggest that the relevant sense of metaphysical well-foundedness is captured either by this idea of being bounded from below or by having a limit, a greatest lower bound. But it turns out that even these may be too strong. This is the key insight in the recent work of Dixon and Rabin &amp; Rabern. If this is right, then we need to have a sense of a metaphysical foundation that is not only compatible with infinite chains of dependence, but also with infinite chains that do not have a lower bound (i.e., “unbounded”  chains).[22]