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 a0), 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?

Answer

You said you wanted an application. Inspired by the example from Exceptional Floating Point, consider the parallel resistance formula:
R_{total} = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2}}
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:
R_{total}=\frac{1}{\frac{1}{0}+\frac{1}{R_2}}=\frac{1}{\infty+\frac{1}{R_2}}=\frac{1}{\infty}=0
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.

Attribution
Source : Link , Question Author : Lorry Laurence mcLarry , Answer Author : imallett

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