Determine Whether Each of the Following Sets Is Countable or Uncountable

question 130

Essay

determine whether each of the following sets is countable or uncountable. For those that are countably infinite exhibit a one-to-one correspondence between the set of positive integers and that set.
-The set of positive rational numbers that can be written with denominators less than 3.

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Definitions:

Utility Function

A symbolic depiction illustrating the ranking of preferences a consumer holds across various goods or outcomes.

Edgeworth Box

A diagram used in economics to show the distribution of resources and the potential gains from trade between two individuals in a pure exchange economy.

Contract Curve

The contract curve represents a set of efficient allocations in the Edgeworth Box, where no participant could be made better off without making another participant worse off.

Pareto Optimal

A condition or situation in which it is impossible to make one party better off without making another party worse off, reflecting an optimal distribution of resources.