Probabilistic Method

The probabilistic method, pioneered by the mathematician Paul Erdos, is a nonconstructive technique used mainly in combinatorics for proving that a mathematical object with some prescribed property exists: if choosing an object at random from a suitable class of objects has a probability greater than zero of having the desired property, then an object with that property must exist, even though the proof never exhibits one directly. Although the argument uses probability, its conclusion that such an object exists is certain rather than merely likely. Beyond combinatorics, the method has been applied in number theory, linear algebra, real analysis, computer science, including randomized rounding algorithms, and information theory. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/