Axiom of completeness states that there are two combinations of commodities available to the consumers, and the consumer has the choice to select a combination. The consumer may have a preference for one commodity than others, or the consumer may be indifferent in choosing between two commodities.

The preference relation of the indifference curve is not complete; it is transitive. Indifference relation has the property of reflexivity and symmetry. In the indifference curve, it is possible that the consumer is not able to choose between the two commodities as the consumer is satisfied by consuming either of the two combinations of goods that lie on the same indifference curves.