Ordered field/Contains Q/Operations and ordering/Exercise

Let $K$ denote an ordered field. We consider the mapping $\mathbb{Z}\to K$ constructed in exercise.

a) Show that this mapping is injective.

b) Show that this mapping can be extended to an injective mapping $\mathbb{Q}\to K$ such that the addition and multiplication in $\mathbb{Q}$ and in $K$ coincide, and such that the ordering of $\mathbb{Q}$ coincides with the ordering of $K$.

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