# Has there ever been an application of dividing by 00?

Regarding the expression $a/0$, according to Wikipedia:

In ordinary arithmetic, the expression has no meaning, as there is no number which, multiplied by $0$, gives $a$ (assuming $a\not= 0$), and so division by zero is undefined.

Is there some other kind of mathematics that is not “ordinary”, where the expression $a/0$ has meaning? Or is the word “ordinary” being used superfluously in the quoted statement?

Is there any abstract application of $a/0$?

You said you wanted an application. Inspired by the example from Exceptional Floating Point, consider the parallel resistance formula:This formula tells you the effective electrical resistance of a path when the current can choose two routes to take.

Let’s pretend that $R_1=0$. Then we have:The resistance being zero is indeed the correct answer; all current flows along the single wire that has no resistance.

Naturally, you need to make appropriate definitions for arithmetic on $\infty$ (i.e., use the projective reals). For well-behaved applications like this, that’s fairly straightforward.