Page "Lossless compression" Paragraph 39

An algorithm that is asserted to be able to losslessly compress any data stream is provably impossible.

While there have been many claims through the years of companies achieving " perfect compression " where an arbitrary number N of random bits can always be compressed to N − 1 bits, these kinds of claims can be safely discarded without even looking at any further details regarding the purported compression scheme.

Such an algorithm contradicts fundamental laws of mathematics because, if it existed, it could be applied repeatedly to losslessly reduce any file to length 0.

Allegedly " perfect " compression algorithms are usually called derisively " magic " compression algorithms.