# Collection of All Ordered Sets is not Set

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## Theorem

Let $\mathrm {OS}$ denote the collection of all ordered sets.

Then $\mathrm {OS}$ is not a set.

## Proof

## 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: Exercise $25$