even if the number of goods is finite, the quantity chosen can be any real number on an interval. A commonly specified Choice Set in Consumer Choice is , where is the number of goods. In this case, there exists a continuous utility function to represent a consumer's preferences if and only if the consumer's preferences are complete, transitive and continuous. Applications Utility is usually applied by economists to such constructs as the indifference curve, which plot the combination of commodities that an individual would accept to maintain a given level of satisfaction. Utility and indifference curves are used by economists to understand the causes of demand curves as part of supply and demand analysis, which is used to analyze the workings of goods markets. A diagram of a general indifference curve is shown below (Figure 1). The vertical axes and the horizontal axes represent an individual's consumption of commodity Y and X respectively. All the combinations of commodity X and Y along the same indifference curve are regarded indifferently by individuals, which means all the combinations along an indifference curve result in the same value of utility. Individual utility and social utility can be construed as the value of a utility function and a social welfare function respectively. When coupled with production or commodity constraints, by some assumptions these functions can be used to analyze Pareto efficiency, such as illustrated by Edgeworth boxes in contract curves. Such efficiency is a major concept in welfare economics. In finance, utility is applied to generate an individual's price for an asset known as the indifference price. Utility functions are also related to risk measures, with the most common example being the entropic risk measure. For artificial intelligence, utility functions are used to convey the value of various outcomes to intelligent agents. This allows the agents to plan actions with the goal of maximizing the utility (or "value") of available choices. Preference Preference, as human's specific likes and dislikes, is used primarily when individuals make choices or decisions among different alternatives. Individual preferences are influenced by various factors such as geographical location, gender, cultures and education. The ranking of utility indicates individuals’ preferences. Although preferences are the conventional foundation of microeconomics, it is often convenient to represent preferences with a utility function and analyze human behavior indirectly with utility functions. Let X be the consumption set, the set of all mutually-exclusive baskets the