What happens if an indifference curve cross itself?

If an indifference curve crosses itself, it violates the assumption of transitivity in consumer preferences. This would imply that the same bundle of goods provides two different levels of utility, leading to inconsistencies in consumer choice. In essence, it suggests that a consumer would be indifferent between two different consumption points that should not be considered equal, which is not rational behavior. Therefore, indifference curves are typically assumed to be convex and never cross.