Order

A set is ordered if every element can be compared with one another:

Order

A set is ordered if, given two elements r,s from the set, exactly one of the following is true:

  1. r<s
  2. r=s
  3. r>s
    We also require transitivity, namely x,y,z in the set and given x<y and y<z, then x<z.

For instance, Q is ordered.

References

  1. [[Abbott Real Analysis.pdf#page=16]]