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== Zero divided by zero ==
== Zero divided by zero ==


The identity <source lang=apl inline>×z</source> {{←→}} <source lang=apl inline>z÷|z</source> holds only when <source lang=apl inline>z</source> is not zero in most APLs. In "Zero Divided by Zero"<ref>[[Eugene McDonnell|McDonnell, Eugene]]. ["https://www.jsoftware.com/papers/eem/0div0.htm" Zero Divided by Zero]. [[APL76]].</ref>, [[Eugene McDonnell]] gave this identity as a reason to define <source lang=apl inline>0÷0</source> to be equal to <source lang=apl inline>0</source>. In [[J]], which took McDonnell's suggestion, the identity always holds.
The identity <source lang=apl inline>×z</source> {{←→}} <source lang=apl inline>z÷|z</source> holds only when <source lang=apl inline>z</source> is not zero in most APLs. In "Zero Divided by Zero"<ref>[[Eugene McDonnell|McDonnell, Eugene]]. [https://www.jsoftware.com/papers/eem/0div0.htm "Zero Divided by Zero"]. [[APL76]].</ref>, [[Eugene McDonnell]] gave this identity as a reason to define <source lang=apl inline>0÷0</source> to be equal to <source lang=apl inline>0</source>. In [[J]], which took McDonnell's suggestion, the identity always holds.


== External links ==
== External links ==

Revision as of 14:58, 27 March 2020

×

Signum (×), Sign, Sign of, or Direction is a monadic primitive function which returns the sign of a real or complex number. That is, it returns 0 when given an argument of 0, and otherwise returns a number with magnitude 1 given by dividing the argument by its own magnitude.

Examples

The three possible results of Signum on a real argument are 0, 1, and ¯1. 

      × ¯3 0 5
¯1 0 1

In dialects with complex numbers, Signum is a somewhat more complicated function, and may return any unit complex number. 

      × 3j4
0.6J0.8

The result is still equal to the original number divided by its magnitude: 

      | 3j4
5
      3j4 ÷ | 3j4
0.6J0.8

The magnitude of the result for a non-zero argument is always 1. 

      | × 3j4 ¯2j1 6j¯7
1 1 1

Zero divided by zero

The identity ×z z÷|z holds only when z is not zero in most APLs. In "Zero Divided by Zero"[1], Eugene McDonnell gave this identity as a reason to define 0÷0 to be equal to 0. In J, which took McDonnell's suggestion, the identity always holds.

External links

Documentation

References

  1. ↑ McDonnell, Eugene. "Zero Divided by Zero". APL76.
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