natural numbers identified with binary strings

It is convenient to identify a natural numberMathworldPlanetmath n with the nth 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 relationMathworldPlanetmath: the nth 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 log(n+1).

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