Definition:Ordering/Strict vs. Weak

Ordering: Strict vs. Weak

Some sources define an ordering as we on $\mathsf{Pr} \infty \mathsf{fWiki}$ define a strict ordering.

Hence, in contrast with such a strict ordering, the term weak ordering is often used in this context to mean what we define on $\mathsf{Pr} \infty \mathsf{fWiki}$ as an ordering.

It is essential to be aware of the precise definitions used by whatever text is being studied so as not to fall into confusion.

Sources

• 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics ... (previous) ... (next): Part $1$: Not Entirely Naive Set Theory: Chapter $2$: Partial Order Relations: Mathographical Remarks