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YCor
YCor
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Euclidean Functionfunction of Euclidean domain defined at 0

Added "teaching" tag because the question is motivated by teaching concerns (question was bumped)
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gmvh
gmvh
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In a few places where I have looked the Euclidean Function of a Euclidean Domain is only being defined for non-zero elements. I am teaching an undergraduate course and I am trying to make things simpleras simple as possible. Is there any good reason why not to define it as $0$ at $0$?

In a few places where I have looked the Euclidean Function of a Euclidean Domain is only being defined for non-zero elements. I am teaching an undergraduate course and I am trying to make things simpler as possible. Is there any good reason why not to define it as $0$ at $0$?

In a few places where I have looked the Euclidean Function of a Euclidean Domain is only being defined for non-zero elements. I am teaching an undergraduate course and I am trying to make things as simple as possible. Is there any good reason why not to define it as $0$ at $0$?

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Yiftach Barnea
Yiftach Barnea
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Euclidean Function at 0

In a few places where I have looked the Euclidean Function of a Euclidean Domain is only being defined for non-zero elements. I am teaching an undergraduate course and I am trying to make things simpler as possible. Is there any good reason why not to define it as $0$ at $0$?