I dont understand of the proof on Bachman's book ''Introduction to p-adic numbers and valuation theory''. (Page 3)
if $\mid x \mid_p \leq 1$ then $\mid 1+x \mid_p \leq 1.$
2026-04-02 09:26:48.1775122008
p adic valuation strong triangle inequality
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What does the triangle inequality tell you? The fact that $|x|_p\leq 1$ tells you that $v_p(x)\geq 0$. Then $v_p(1)=0 (Why?)$. We also know that $v_p(a+x)\geq \min \{v_p(a), v_p(x)\}$. Can you conclude the result from this?