# Term or notation for a sequence in reverse order?

• Mar 13th 2011, 02:01 PM
Term or notation for a sequence in reverse order?
If you have a sequence a={1,0,2,1,3} and a sequence b={3,1,2,0,1}, the sequence b is sequence a in reverse order. Is there a term to describe or a way to denote sequence b in terms of a? I was thinking maybe, b is the inverse of a or reverse of a? or b={a}^{-1}?

Thanks
• Mar 13th 2011, 02:44 PM
DrSteve
Technically a sequence is a function from the natural numbers to some other set A. Thus the inverse of a sequence (if it exists) would be a map from A to the naturals. So it's unlikely that you would want to use the inverse notation for this. I am not familiar with any standard notation here, so feel free to make up your own.
• Mar 14th 2011, 02:34 AM
Ackbeet
You could just write

$\displaystyle \{b_{j}\}=\{a_{\text{len}\{a\}-j}\},$

where $\displaystyle \text{len}\{a\}$ is the length of the sequence $\displaystyle \{a_{j}\},$ assuming it's finite. Indeed, what you're asking to do here is not possible for infinite sequences (where would you start?).

You'll also note that I'm assuming the first term in the sequence has index zero.