A poset (R, ≼) is well-founded if there is no infinite decreasing sequence of elements in the poset, that is, elements x1, x2, …, xn such that ⋯<xn<⋯<x2<x1, A poset (R, ≼) is dense if for all x ∈S and y ∈S with x<y, there is an element z ∈R such that x<z<y. Show that a poset is well-ordered if and only if it is totally ordered and well-founded. | Numerade
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