Interleave sequence

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In mathematics, an interleave sequence is obtained by merging two sequences via an in shuffle.

Let be a set, and let and , be two sequences in The interleave sequence is defined to be the sequence Formally, it is the sequence given by

Properties[edit]

  • The interleave sequence is convergent if and only if the sequences and are convergent and have the same limit.[1]
  • 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 (0, 1)×(0, 1) to the interval (0, 1). Different radixes give rise to different injections; the one for the binary numbers is called the Z-order curve or Morton code.[2]

References[edit]

  1. ^ Strichartz, Robert S. (2000), The Way of Analysis, Jones & Bartlett Learning, p. 78, ISBN 9780763714970.
  2. ^ Mamoulis, Nikos (2012), Spatial Data Management, Synthesis lectures on data management, 21, Morgan & Claypool Publishers, pp. 22–23, ISBN 9781608458325.

This article incorporates material from Interleave sequence on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.