existence and uniqueness theorem

The existence and uniqueness theorem states that for certain mathematical problems—specifically differential equations—if specific conditions are met, then there is exactly one solution that fits those conditions. In simpler terms, it guarantees that, under those conditions, a problem has one and only one answer, ensuring predictability and reliability of solutions. This theorem is fundamental in mathematics and science because it confirms that the models or equations used to describe real-world phenomena have a definite, unique solution that accurately represents the situation.