
Compressing random data – a preliminary algorithm - Uptrenda
http://roberts.pm/compressing_random_data_part_1
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eesmith
[https://en.wikipedia.org/wiki/Pigeonhole_principle#Uses_and_...](https://en.wikipedia.org/wiki/Pigeonhole_principle#Uses_and_applications)

> 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.

