| Version 4 |
Version 3 |
| A binary relation $\mathcal{R}$ on a set $A$ is said to be \emph{irreflexive} if $\forall a\in A$, $\neg a\mathcal{R} a$. In other words, ``no element is $\mathcal{R}$-related to itself." |
A binary relation $\mathcal{R}$ on a set $A$ is said to be \emph{irreflexive} if $\forall a\in A$, $\neg a\mathcal{R} a$. In other words, ``no element is $\mathcal{R}$-related to itself." |
|
|
| For example, the relation $<$ (``less than") is an irreflexive relation on the set of natural numbers. |
For example, the relation $<$ (``less than") is an irreflexive relation on the set of natural numbers. |
|
|
| Note that ``irreflexive" is not simply the negation of ``\PMlinkname{reflexive}{Reflexive} |
Note that ``irreflexive" is not simply the negation of ``reflexive." Although it is impossible for a relation (on a nonempty set) to be both reflexive and irreflexive, it is easy to come up with relations that are neither. |
| ." Although it is impossible for a relation (on a nonempty set) to be both reflexive and irreflexive, it is easy to come up with relations that are neither. |
|
