Is there a math operator for a safe division, returning a pre-set value, usually 0, when divide by zero is encountered? If not, in a computer science or mathematics paper would one just say before an equation that all divisions are "safe"?
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In a paper, it's best to preface a formula or argument that has potential divisions-by-zero by stating clearly why the circumstances causing such a division can be reasonably ignored (eg, a triangle is degenerate) or that they represent a special case one can handle separately (eg, a triangle is equilateral). Introducing a "safe division" operator burdens the reader with believing/verifying that whatever formulas or arguments you present remain valid even when problematic divisions are replaced by your arbitrary "pre-set value". It shouldn't be used as a free pass to divide recklessly. – Blue Aug 06 '20 at 02:21
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This is equivalent to defining an operation $\widetilde{\div}:\mathbb{R}\times\mathbb{R}\to\mathbb{R}$ with $a\widetilde{\div}b=a/b$ when $b\neq0$ and $a\widetilde{\div}b=0$ when $b=0$. There is no commonly used operation that I know of that does this, but you could define one such as this very easily. If you are going to use this in a paper I would make sure to clarify that you are using a different definition of division but it shouldn’t cause any other issues so long as it is clear what your definition is.
csch2
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What professors at my university did, was to say terms where division by zero ocurred, they labeled them "non-physical" and therefore removed them. Infinity for example, is not possible in some physical realm and such has to be corrected, i.e. removed.
Mikael Helin
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