Statically, how is the compression of a file possible? As in, a file n bytes long can have $2^{n*8}$ (the 'times 8' part is because there are 8 bits in a byte). So, if you decrease the size then statistically it shouldn't not possible to decrease a file's size (compress it) and be able to perfectly reassemble the original file because the total number of different possibilities for the input will be greater than the output, so u cant exactly get the input from the output.
So, what is going on (in statistical terms)!?!?!?!
Please note that I am not trying to disprove compression (I ♥∞ compression (because I am a programmer)), I just want to know the statistics behind it.
You have essentially rediscovered the theorem that says that any faithful compression algorithm must increase the size of some input files in order to compress others - one hopes, most others.
Google
for several links.
https://en.wikipedia.org/wiki/Pigeonhole_principle#Uses_and_applications
http://matt.might.net/articles/why-infinite-or-guaranteed-file-compression-is-impossible/
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