Let R be an ordered ring and consider the ring R[x. y] of polynomials in two variables with coefficients in R. Example 25.2 describes two ways in which we can order R[x], and for each of these, we can continue on and order (R[x])[y] in the analogous two ways, giving four ways of arriving at an ordering of R[x, y]. There are another four ways of arriving at an ordering of R[x, y] if we first order R[y] and then (R[y])[x]. Show that all eight of these orderings of R[x, y] are different. [Hint: You might start by considering whether x
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