Question

If we prove a theorem by examining a relatively small number of examples, or cases, that span all possibilities that this theorem addresses, this is a

Answer 1

Proof by exhaustion is a method used in mathematics to establish the validity of a theorem by systematically examining all possible cases or examples. It is a reliable technique when other methods are not feasible.

Step-by-step explanation:

The process described in the question is known as proof by exhaustion in the field of mathematics. This method involves systematically examining all possible cases or examples that the theorem addresses in order to establish its validity.

For example, consider proving that a certain statement is true for all even numbers. To use proof by exhaustion, you would examine a representative sample of even numbers, such as 2, 4, 6, and so on, ensuring that the statement holds true for each one. By covering all possibilities, you can confidently conclude that the statement is true for all even numbers.

Proof by exhaustion is a reliable technique when it is not feasible to prove a theorem using other methods, such as mathematical induction or deductive reasoning.