Describe an ordering of the ring Q[], discussed in Example 25.11, in which is greater than

Describe an ordering of the ring Q[π], discussed in Example 25.11, in which π is greater than any rational number.

Data from in Example 25.11

Example 22.9 stated that the evaluation homomorphism ∅π : Q[x]→ R where 

∅(a₀ + a₁x + · · · + a_nxⁿ) = a₀ + a₁π + · · · + a_nπⁿ 

is one to one. Thus it provides an isomorphism of Q[x] with ∅[Q[x]]. We denote this image ring by Q[π]. If we provide Q[x] with the ordering using the set P_low of Examples 25.2 and 25.6, the ordering on Q[π] induced by ∅_π is very different from that induced by the natural (and only) ordering of R In the P_low ordering, π is less than any element of Q!