A total-ordered set is a LatticE (T,v,^) where for any a,b in T, either avb=a and a^b=b, or avb=b and a^b=a. A PartialOrder <= on a set T defines a total order if and only for every a,b in T, exactly one of the following hold: |

A total-ordered SeT is a LatticE (T,v,^) where for any a,b in T, either avb=a and a^b=b, or avb=b and a^b=a. A PartialOrder <= on a set T defines a total order if and only for every a,b in T, exactly one of the following hold: |

The unique smallest total-ordered set with neither an upper nor lower bound is the IntegerNumbers. The unique smallest unbounded total-ordered set which also happens to be dense, that is have non-empty (a,b) for every a<b, is the RationalNumbers. The unique smallest unbounded connected total-ordered set is the RealNumbers?. |

The unique smallest total-ordered set with neither an upper nor lower bound is the IntegerNumbers. The unique smallest unbounded total-ordered set which also happens to be dense, that is have non-empty (a,b) for every a<b, is the RationalNumbers. The unique smallest unbounded connected total-ordered set is the RealNumbers?. |