Definition:Many-to-One Relation/Also known as

Many-to-One Relation: Also known as

A many-to-one relation is also referred to as:

a rule of assignment

a functional relation

a right-definite relation

a right-unique relation

a partial mapping.

Some sources break with mathematical convention and call this a (partial) function.

These sources subsequently define a total function to be what on $\mathsf{Pr} \infty \mathsf{fWiki}$ is called a mapping.

None of these names is as intuitively obvious as many-to-one relation, so the latter is the preferred term on $\mathsf{Pr} \infty \mathsf{fWiki}$.

However, it must be noted that a one-to-one relation is an example of a many-to-one relation, which may confuse.

The important part is the to-one part of the definition, which is as opposed to the to-many characteristic of a one-to-many relation and a many-to-many relation.

Also defined as

Some approaches, for example 1999: András Hajnal and Peter Hamburger: Set Theory, define a mapping as a many-to-one relation from $S$ to $T$, and then separately specify its requisite left-total nature by restricting $S$ to the domain.

However, this approach is sufficiently different from the mainstream approach that it will not be used on $\mathsf{Pr} \infty \mathsf{fWiki}$ and limited to this mention.