Is there a method to compress all data without loss (lossless compression)?
There are $2^n$ bitstrings of length $n$, but only $2^n-1$ bitstrings of length smaller than $n$. Hence there is no one-to-one mapping which maps every bitstring of length $n$ to a bitstring of strictly smaller length. In other words, for any (lossless) compression scheme there will always be a string which it doesn't compress.