Editing Indifference curve (section)

=== Preference relations ===
Let
:<math>A\;</math> be a set of mutually exclusive alternatives among which a consumer can choose.
:<math>a\;</math> and <math>b\;</math> be generic elements of <math>A\;</math>.
In the language of the example above, the set <math>A\;</math> is made of combinations of apples and bananas. The symbol <math>a\;</math> is one such combination, such as 1 apple and 4 bananas and <math>b\;</math> is another combination such as 2 apples and 2 bananas.

A preference relation, denoted <math>\succeq</math>, is a [[binary relation]] define on the set <math>A\;</math>.

The statement
:<math>a\succeq b\;</math>
is described as '<math>a\;</math> is weakly preferred to <math>b\;</math>.' That is, <math>a\;</math> is at least as good as <math>b\;</math> (in preference satisfaction).

The statement
:<math>a\sim b\;</math>
is described as '<math>a\;</math> is weakly preferred to <math>b\;</math>, and <math>b\;</math> is weakly preferred to <math>a\;</math>.' That is, one is ''indifferent'' to the choice of <math>a\;</math> or <math>b\;</math>, meaning not that they are unwanted but that they are equally good in satisfying preferences.

The statement
:<math>a\succ b\;</math>
is described as '<math>a\;</math> is weakly preferred to <math>b\;</math>, but <math>b\;</math> is not weakly preferred to <math>a\;</math>.' One says that '<math>a\;</math> is strictly preferred to <math>b\;</math>.'

The preference relation <math>\succeq</math> is '''complete''' if all pairs <math>a,b\;</math> can be ranked. The relation is a [[transitive relation]] if whenever <math>a\succeq b\;</math> and <math>b\succeq c,\;</math> then <math>a\succeq c\;</math>.

For any element <math>a \in A\;</math>, the corresponding indifference curve, <math>\mathcal{C}_a</math> is made up of all elements of <math>A\;</math> which are indifferent to <math>a</math>.  Formally,

<math>\mathcal{C}_a=\{b \in A:b \sim a\}</math>.