ORDINAL THEORY:

INDIFFERENCE CURVE APPROACH In indifference curve approach consumer is assumed to be rational, so that consumer's objective is to maximise her utility by choosing a commodity bundle among all other available commodity bundles (under budget constraint) where total utility ('U') depends on quantity consumption given her taste and preferences. Therefore, in a two-commodity world (say x₁  and  x₂) utility function is given by U = U (x₁,x₂) and it depends on taste and preferences of the consumer, which is specified by axioms given below:   

Axiom of reflexiveness: Consumer's choice is reflexive. Implication: Weak preference relation is denoted by 'R'. Suppose there are two goods x₁ and x₂ and suppose x1 is weakly preferred to x₂ i.e., x₁Rx₂ which implies that either x1 is strictly preferred over x₂ (it is denoted by x₁Px₂) or x₁ is indifference to x₂ (it is denoted by x₁Ix₂), where 'P' and 'I' implies strict preference relation and indifference respectively. The set constituted by all commodity bundles or vector is known as commodity set (X). Any one commodity bundle is denoted by 'x' is weakly preferred (i.e., either strictly preferred or indifferent) over any other commodity bundle (i.e., in respect to 'x'). Therefore, we have xR_x. Clearly, any one commodity bundle may be indifferent to another commodity bundle i.e., there is a possibility of indifference or same level of utility between the commodity bundles. None of the commodity bundles are not preferred i.e., consumer can choose any commodity bundle. So choice set of this consumer is specified by the commodity set 'X'.