# Category:Order Embeddings

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This category contains results about Order Embeddings.

Definitions specific to this category can be found in Definitions/Order Embeddings.

$\phi$ is an **order embedding of $S$ into $T$** if and only if:

- $\forall x, y \in S: x \preceq_1 y \iff \map \phi x \preceq_2 \map \phi y$

## Pages in category "Order Embeddings"

The following 15 pages are in this category, out of 15 total.

### E

### M

- Mapping from Totally Ordered Set is Dual Order Embedding iff Strictly Decreasing
- Mapping from Totally Ordered Set is Order Embedding iff Strictly Increasing
- Mapping from Totally Ordered Set is Order Embedding iff Strictly Increasing/Reverse Implication
- Mapping from Totally Ordered Set is Order Embedding iff Strictly Increasing/Reverse Implication/Proof 1
- Mapping from Totally Ordered Set is Order Embedding iff Strictly Increasing/Reverse Implication/Proof 2