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Compressing random data – a preliminary algorithm
- eesmith 7y agohttps://en.wikipedia.org/wiki/Pigeonhole_principle#Uses_and_applications https://en.wikipedia.org/wiki/Pigeonhole_principle#Uses_and_... > The principle can be used to prove that any lossless compression algorithm, provided it makes some inputs smaller (as the name compression suggests), will also make some other inputs larger. Otherwise, the set of all input sequences up to a given length L could be mapped to the (much) smaller set of all sequences of length less than L without collisions (because the compression is lossless), a possibility which the pigeonhole principle excludes.