# Ascending tuples of integers

Hi everyone,

I'm trying to define the set of all tuples of ascending integers (any length, repetitions allowed). What is the best way to do this? Do I use Family()? I'd like to use this set enumerate the basis of a combinatorial free algebra.

Bonus question: Is it possible to add an extra label to each integer in the tuple?

Isn't this equivalent to the set of tuples of non-negative integers via the correspondence (x0,x1,x2,x3,...,xk) <-> (x0,x1-x0,x2-x1,x3-x2,...,xk-x[k-1]) (I guess you can allow x0 to be negative if that fits your description)