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Ordered field/Properties of powers/Exercise
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Show that in an
ordered field
the following properties hold.
We have
a
2
≥
0
{\displaystyle {}a^{2}\geq 0}
.
If
a
≥
b
≥
0
{\displaystyle {}a\geq b\geq 0}
holds, then also
a
n
≥
b
n
{\displaystyle {}a^{n}\geq b^{n}}
holds for all
n
∈
N
{\displaystyle {}n\in \mathbb {N} }
.
From
a
≥
1
{\displaystyle {}a\geq 1}
we get
a
n
≥
a
m
{\displaystyle {}a^{n}\geq a^{m}}
for integer numbers
n
≥
m
{\displaystyle {}n\geq m}
.
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