The probabilistic method is a nonconstructive method, primarily used in combinatorics and pioneered by Paul Erdős, for proving the existence of a prescribed kind of mathematical object. It works by showing that if one randomly chooses objects from a specified class, the probability that the result is of the prescribed kind is more than zero. Although the proof uses probability, the final conclusion is determined for certain, without any possible error.
This method has now been applied to other areas of mathematics such as number theory, linear algebra, and real analysis, as well as in computer science (e.g. randomized rounding).
Read more about Probabilistic Method: Introduction, Two Examples Due To Erdős
Famous quotes containing the word method:
“... the one lesson in the ultimate triumph of any great actress has been to enforce the fact that a method all technique or a method all throes, is either one or the other inadequate, and often likely to work out in close proximity to the ludicrous.”
—Mrs. Leslie Carter (1862–1937)