Convergence of a sequence in a non-Archimdean valuation for a field.
$$|x|> |y| \implies |x+y| = |x|$$
Proof: if $|x+y|< |x|$ then $$|x| =|x+y-y| \le \max(|x+y|,|y|)<|x|$$
Convergence of a sequence in a non-Archimdean valuation for a field.
$$|x|> |y| \implies |x+y| = |x|$$
Proof: if $|x+y|< |x|$ then $$|x| =|x+y-y| \le \max(|x+y|,|y|)<|x|$$