Interleave sequence

Properties

• The interleave sequence is convergent if and only if the sequences and are convergent and have the same limit.
• Consider two real numbers a and b greater than zero and smaller than 1. One can interleave the sequences of digits of a and b, which will determine a third number c, also greater than zero and smaller than 1. In this way one obtains an injection from the square × to the interval. Different radixes give rise to different injections; the one for the binary numbers is called the Z-order curve or Morton code.