Math operator for safe division

Question

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"?

Answer 1

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.

Answer 2

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.