 An obvious generalisation of Ducci sequences is to allow the members of the "n"-tuples to be "any" real numbers rather than just integers.For example,
formula_6
formula_7

The properties presented here do not always hold for these generalisations.For example, a Ducci sequence starting with the "n"-tuple (1, "q", "q"2, "q"3) where "q" is the (irrational) positive root of the cubic formula_8 does not reach (0,0,0,0) in a finite number of steps, although in the limit it converges to (0,0,0,0).