I have come across a bit of folklore(?) which goes something like ``given any finite sequence of numbers, there is more than one valid way of continuing the sequence''. For example see <a href="http://www.guardian.co.uk/books/2005/feb/05/featuresreviews.guardianreview13">here</a>. I would like to know if this is actually stated and proved rigorously, and if so, where can I find a statement and proof?