N is a positive integer I suppose? If I'm understanding you correctly, then yes, your definitions work, except that you didn't mention that the set has a least element, for which A(n-1) is not defined.

Ordered sets are usually referred to as tuples. (Ordered pair is another name for 2-tuple, an ordered triple is a 3-tuple, etc.)

Note that since you're

*given* the subset of the reals rather than trying to

*construct* the set, you could use a simpler definition. These following definitions are equivalent:

Let

. Let the N-tuple

be an ordering of the elements of

.

Definition 1:

is in sequential order

.

Definition 2:

is in sequential order

.

Definition 3:

is in sequential order

.