# Half characteristic function

The **half characteristic function** or **partial characteristic function** is a function of mathematics that identifies a set . It is defined as follows:

- .

As you can see, all the “magic” of the function is in the definition domain. Now if A is a subset of a larger set B, so χ 'is _{A} to B \ A undefined. We then get:

## Semi-decidability

Half the characteristic function can name all elements on B that belong to A, but cannot really exclude elements that do not belong to A. One speaks of χ ' _{A} being partial. If χ ' _{A is} also computable, then A is called *semi-decidable* or recursively enumerable , since all elements can be enumerated, but the elements B \ A cannot be excluded. For this one needs the characteristic function , which is total.