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Completeness Axiom

Requires that for any two bundles, A and B, the consumer can always state a preference (A \succ B, B \succ A, or A \sim B). This ensures the preference relation is well-defined.
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The statement of the theorem

For any two bundles AX\mathbf{A} \in X and BX\mathbf{B} \in X, the preference relation \succ must satisfy the completeness property: AB\mathbf{A} \succ \mathbf{B} or BA\mathbf{B} \succ \mathbf{A} or AB\mathbf{A} \sim \mathbf{B}.