Thread: calculating distance between members of a set

Hi,

I'm wondering if anyone can help me please, i'm wanting to know the mathematical notation for representing calculating the ditancaes of a set. What i want is a new set with the distances.

e.g. i have an ordered set X = {1,5,12,15,25}

the distance would be |Xi - Xi+1|

how can i represent in mathematical terms a new set that contains the distances of the set X.

e.g. in pseudo code it would look like

Set X = new Set{1,5,12,15,25}
Set Y = new Set() // for the distances

for(i = 0; i < X.length -1; ++i)
{
Y.Add(X[i] - X[i+1])
}


What i want would be the math notation for obtaining set Y

Thanks.

If |X| represents the number of elements in X and x[i] represents the ith element of X, would Y = {|x[i]-x[i+1]| : i in {1, ..., |X|-1}} work?

I think thats right, thanks.