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http://en.wikipedia.org/wiki/Data_compression#Lossless_data_compression
For any given compression scheme, one can provide sample input that would result in no savings in space, right?
Yes, there’s always something that will grow larger. The pigeonhole principle says that if you have a space of inputs, and a 1-to-1 function (the lossless compression), then the number of outputs has to be the same as the number of inputs.
If the inputs are files of N bits, then the number of inputs is
2**N, and the number of outputs is2**N. You can’t store that many different outputs in files all shorter than N bits.