For a Euclidean Domain, prove that $\delta(z)>0$ if $z\in R$ is not a unit, where $\delta$ is the Euclidean function.
Is it just since $z$ is not a unit then $\delta(z)>\delta(1)>0?$
Please help, thanks!
2026-03-29 19:17:26.1774811846
For a Euclidean Domain, prove that $\delta(z)>0$ if $z\in R$ is not a unit.
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We can write $1=aq+r$ with $r\ne 0$ (otherwise $a$ would be invertible), so $0\le\delta(r)<\delta(a)$.