You can make that more concise too. An ideal compressor would be able to map every string of length n to a string of length m<n and back. Since a bijection requires that its source and target sets are of the same cardinality, and there are more strings of length m than length n, this compressor cannot be a bijection. Or even more concisely: you can't fit 10 pigeons into 9 pigeonholes unless one pigeon shares.