Equal to

is a comparison function which tests whether argument elements are tolerantly equal to each other: it returns 1 if the elements being compared match and 0 if they do not. It is the negation of Not Equal to.

APL's  differs from the usage of $$=$$ in traditional mathematical notation by having an implied Iverson bracket. Thus,  is APL is equivalent to $$[i=j]$$ or $$\delta_{ij}$$ (Kronecker delta) in mathematics.

Examples
Equal to compares arrays one element at a time, returning 1 when elements match and 0 when they do not. It is subject to comparison tolerance: floating-point numbers which are very close together are considered equal, even though they are slightly different: In a nested APL, Equal to is pervasive, and compares all simple scalars found in a nested array. In a flat array language such as J, it instead compares Boxes directly, since they are the elements of a boxed array.

Boolean function
When the arguments to Equal to are Boolean, it is the Logical biconditional function, or the negation of the xor function (which is Not Equal to restricted to Boolean arguments): In the context of logic, it can be read as if and only if. This function is also known as xnor or the Kronecker delta.

Reduction with  is the same as reduction with xor, but inverted if the number of reduced elements is even. The left and right identity element for Boolean  is 1.

Documentation

 * Dyalog
 * APLX
 * J Dictionary, NuVoc