Equaliser (mathematics) - Difference Kernels

Difference Kernels

A binary equaliser (that is, an equaliser of just two functions) is also called a difference kernel. This may also be denoted DiffKer(f,g), Ker(f,g), or Ker(fg). The last notation shows where this terminology comes from, and why it is most common in the context of abstract algebra: The difference kernel of f and g is simply the kernel of the difference fg. Furthermore, the kernel of a single function f can be reconstructed as the difference kernel Eq(f,0), where 0 is the constant function with value zero.

Of course, all of this presumes an algebraic context where the kernel of a function is its preimage under zero; that is not true in all situations. However, the terminology "difference kernel" has no other meaning.

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