Proof by contradiction is a mathematical method where you assume the opposite of what you want to prove, and then show that this assumption leads to a contradiction, thereby proving the original statement. This technique is particularly useful when direct proof is difficult or when dealing with statements involving negations or inequalities.
Mathematical existence is a foundational concept in mathematics and logic that describes the conditions under which an object, number, or function is considered to exist within a given mathematical system. It often concerns proving the existence of a solution to an equation or a set satisfying certain properties without necessarily constructing the solution itself.