Ordered field/Properties of powers/Exercise

Show that in an ordered field the following properties hold.

1. We have ${}a^{2}\geq 0$.
2. If ${}a\geq b\geq 0$ holds, then also ${}a^{n}\geq b^{n}$ holds for all ${}n\in \mathbb {N}$.
3. From ${}a\geq 1$ we get ${}a^{n}\geq a^{m}$ for integer numbers ${}n\geq m$.

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