natural numbers identified with binary strings

It is convenient to identify a natural number $n$ with the $n$th binary string in lexicographic order:

The more common binary notation for numbers fails to be a bijection because of leading zeroes. Yet, there is a close relation: the $n$th binary string is the result of stripping the leading 1 from the binary notation of $n+1$.

With this correspondence in place, we can talk about such things as the length $l(n)$ of a number $n$, which can be seen to equal $\lfloor \log (n+1)\rfloor$.

Title	natural numbers identified with binary strings
Canonical name	NaturalNumbersIdentifiedWithBinaryStrings
Date of creation	2013-03-22 13:43:44
Last modified on	2013-03-22 13:43:44
Owner	tromp (1913)
Last modified by	tromp (1913)
Numerical id	7
Author	tromp (1913)
Entry type	Definition
Classification	msc 68Q30