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The article points out how rational numbers are the needles amongst the hay of irrational numbers. In a more discrete setting, we have compressible files being

by tromp 8y ago

The article points out how rational numbers are the needles amongst the hay of irrational numbers. In a more discrete setting, we have compressible files being the needles among the hay of incompressible files. Technically; all but a fraction of 2^-k of binary strings of length n need at least n-k bits to describe, but we cannot come up with a single explicit example.

adrianN 8y ago
For any fixed compression scheme it's trivial to come up with files that don't compress.
- baking 8y ago
  But any file that is "trivial to come up with" is going to be easy to compress under many other schemes.
  - tromp 8y ago
    Indeed; we can't come up with explicit examples for the uncomputable compression to the shortest possible description (corresponding to the Kolmogorov complexity).