Proposition: A Field with an Absolute Value is a Metric Space

Let $(F,+,\cdot)$ be a field with an absolute value $|\dot|$ define on it. Then the function $d:F\times F\to\mathbb R$ defined by $$d(x,y):=|x-y|$$ defines a metric, making $(F,d)$ a metric space.

Proofs: 1

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