Historical Notes
The fact that every non-negative integer has a unique representation in bijective base-k (k ≥ 1), is a "folk theorem" that has been rediscovered many times. Early instances are Smullyan (1961) for the case k = 2, and Böhm (1964) for all k ≥ 1 (the latter using these representations to perform computations in the programming language P′′). Knuth (1969) mentions the special case of k = 10, and Salomaa (1973) discusses the cases k ≥ 2. Forslund (1995) considers that if ancient numeration systems used bijective base-k, they might not be recognised as such in archaeological documents, due to general unfamiliarity with this system. (The latter article is notable in that it does not cite existing literature on this system, but appears to unwittingly reinvent it.)
Read more about this topic: Bijective Numeration
Famous quotes containing the words historical and/or notes:
“This seems a long while ago, and yet it happened since Milton wrote his Paradise Lost. But its antiquity is not the less great for that, for we do not regulate our historical time by the English standard, nor did the English by the Roman, nor the Roman by the Greek.... From this September afternoon, and from between these now cultivated shores, those times seemed more remote than the dark ages.”
—Henry David Thoreau (1817–1862)
“The drama critic on your paper said my chablis-tinted hair was like a soft halo over wide set, inviting eyes, and my mouth, my mouth was a lush tunnel through which golden notes came.”
—Samuel Fuller (b. 1911)