- Interleave sequence
In
mathematics , an interleave sequence is obtained by merging together twosequence s.Let S be a set, and let x_i) and y_i), i=0,1,2,..., be two
sequence s in S. The "interleave sequence" is defined to be the sequence x_0, y_0, x_1, y_1, dots. Formally, it is the sequence z_i), i=0,1,2,... given by:z_i := left{egin{matrix} x_k & mbox{ if } i=2k mbox{ is even,}\ y_k & mbox{ if } i=2k+1 mbox{ is odd.} end{matrix} ight.
Properties
* The interleave sequence z_i) is convergent
if and only if the sequences x_i) and y_i) are convergent and have the same limit.* Consider two
real number s "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).
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