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How do I describe the joining of two finite sequences in mathematical notation? For example, suppose the following:

$$ A=(a_i)_{i=1,2}=(4,2)\\ B=(b_i)_{i=1,2}=(9,5)\\ C=(c_i)_{i=1,...,4}=(4,2,9,5) $$

Sequence $C$ can be considered sequence $A$ with sequence $B$ attached to the end. How do I describe sequence $C$ in terms of sequence $A$ and $B$?


marked as duplicate by Lord_Farin, Stefan Hansen, Amzoti, user67258, Myself Jun 18 '13 at 14:37

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  • 1
    $\begingroup$ It's the concatenation. $\endgroup$ – Gerry Myerson Jun 18 '13 at 13:04
  • $\begingroup$ $C= A \cup B$. There is no "attaching to the end". Sets are not ordered. $\endgroup$ – mjb Jun 18 '13 at 13:07
  • $\begingroup$ @mjb I'm a bit confused. Why wouldn't a sequence be considered ordered? $\endgroup$ – Vilhelm Gray Jun 18 '13 at 13:10
  • $\begingroup$ @VilhelmGray See my answer below. Sequences are ordered, sets are not. Your notation suggests you mean sets. $\endgroup$ – mjb Jun 18 '13 at 13:11
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    $\begingroup$ Cf. #298648. $\endgroup$ – Lord_Farin Jun 18 '13 at 13:16

Those are sets, not sequences. If you ment sets, then it is $C = A \cup B$, the union of the two sets.

If you ment finite sequences you could write \begin{equation} c_i = \begin{cases} a_i & i=1,2 \\ b_{i-2} & i=3,4 \end{cases} \end{equation}

  • $\begingroup$ I'm sorry, I must have inadvertently used the notation for sets; I do mean sequences however. I want to correct the notation in my question, but I'm not sure what the correct notation for sequences are -- do I just remove the curly braces? $\endgroup$ – Vilhelm Gray Jun 18 '13 at 13:12
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    $\begingroup$ Then the correct notation would be: $A=(a_i)_{i=1,2}=(4,2)$, $B=(b_i)_{i=1,2}=(9,5)$ and $C=(c_i)_{i=1,\ldots,4}$ with $c_i$ defined as above. $\endgroup$ – mjb Jun 18 '13 at 13:15
  • $\begingroup$ There are of course more complicated notations by interpreting those sequences as functions $\lbrace 1,2 \rbrace \to \mathbb{R}$ or as aborting elements of $\ell^\infty$. $\endgroup$ – mjb Jun 18 '13 at 13:25

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