# Definition:Ordering/Strict vs. Weak

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## 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