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Ordinal Utility Axiom

States that preferences can be ranked (ordered) without requiring cardinal measurement. If bundle A is preferred to bundle B, A \succ B, which is the core assumption for consumer choice models.
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The statement of the theorem

Let XX be the set of all consumption bundles. The preference relation ≻\succ defined on XX is a binary relation such that for any two bundles A,B∈X\mathbf{A}, \mathbf{B} \in X, the consumer can state A≻B\mathbf{A} \succ \mathbf{B} (A is strictly preferred to B), B≻A\mathbf{B} \succ \mathbf{A} (B is strictly preferred to A), or A∼B\mathbf{A} \sim \mathbf{B} (A is indifferent to B).