Search results
Results From The WOW.Com Content Network
Although the pigeonhole principle appears as early as 1624 in a book attributed to Jean Leurechon, [2] it is commonly called Dirichlet's box principle or Dirichlet's drawer principle after an 1834 treatment of the principle by Peter Gustav Lejeune Dirichlet under the name Schubfachprinzip ("drawer principle" or "shelf principle").
The existence of these polynomials was proven by Axel Thue; [1] Thue's proof used what would be translated from German as Dirichlet's Drawers principle, which is widely known as the Pigeonhole principle. Carl Ludwig Siegel published his lemma in 1929. [2] It is a pure existence theorem for a system of linear equations.
In mathematics, the incompressibility method is a proof method like the probabilistic method, the counting method or the pigeonhole principle.To prove that an object in a certain class (on average) satisfies a certain property, select an object of that class that is incompressible.
This theorem is a consequence of the pigeonhole principle. Peter Gustav Lejeune Dirichlet who proved the result used the same principle in other contexts (for example, the Pell equation) and by naming the principle (in German) popularized its use, though its status in textbook terms comes later. [2] The method extends to simultaneous ...
By operation of the pigeonhole principle, no lossless compression algorithm can shrink the size of all possible data: Some data will get longer by at least one symbol or bit. Compression algorithms are usually effective for human- and machine-readable documents and cannot shrink the size of random data that contain no redundancy. Different ...
The pigeonhole principle states that if a items are each put into one of b boxes, where a > b, then one of the boxes contains more than one item. Using this one can, for example, demonstrate the existence of some element in a set with some specific properties.
Consider the following theorem (which is a case of the pigeonhole principle): If three objects are each painted either red or blue, then there must be at least two objects of the same color. A proof: Assume, without loss of generality, that the first object is red.
The proof that the language of balanced (i.e., properly nested) parentheses is not regular follows the same idea. Given p {\displaystyle p} , there is a string of balanced parentheses that begins with more than p {\displaystyle p} left parentheses, so that y {\displaystyle y} will consist entirely of left parentheses.