Question

define conjecture with an example

Answer 1

A conjecture is a mathematical statement that has not yet been rigorously proved. Conjectures arise when one notices a pattern that holds true for many cases. However, just because a pattern holds true for many cases does not mean that the pattern will hold true for all cases. Conjectures must be proved for the mathematical observation to be fully accepted. When a conjecture is rigorously proved, it becomes a theorem.

A conjecture is an important step in problem solving; it is not just a tool for professional mathematicians. In everyday problem solving, it is very rare that a problem's solution is immediately apparent. Instead, the problem solving process involves analyzing the problem structure, examining cases, developing a conjecture about the solution, and then confirming that conjecture through proof.