# Joining finite sequences [duplicate]

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, MyselfJun 18 '13 at 14:37

• It's the concatenation. – Gerry Myerson Jun 18 '13 at 13:04
• $C= A \cup B$. There is no "attaching to the end". Sets are not ordered. – mjb Jun 18 '13 at 13:07
• @mjb I'm a bit confused. Why wouldn't a sequence be considered ordered? – Vilhelm Gray Jun 18 '13 at 13:10
• @VilhelmGray See my answer below. Sequences are ordered, sets are not. Your notation suggests you mean sets. – mjb Jun 18 '13 at 13:11
• Cf. #298648. – 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 $$c_i = \begin{cases} a_i & i=1,2 \\ b_{i-2} & i=3,4 \end{cases}$$

• 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? – Vilhelm Gray Jun 18 '13 at 13:12
• 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. – mjb Jun 18 '13 at 13:15
• 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 $\ell^\infty$. – mjb Jun 18 '13 at 13:25