I have two questions:(adsbygoogle = window.adsbygoogle || []).push({});

1. Least Upper Bound

ex)

Let A = {x : x∈Q(rational number) , x^2＜2, x＜0} ⊂ S (ordered set),

Then why doesn't the least upper bound (α,which is √2) exist in S?

As long as I know, S is a set which has an order. And it doesn't state whether it belongs to Q(rational number) or R(Real Number)

2. Ordered Set (S)

Whenever I see definition related to least upper bound, greatest lower bound and so forth, I always see 'A⊂S'

For example, let's look at the defintion of 'bounded above' :

Supposed S is an ordered set and A⊂S. If there exists a β∈S such that x≤β for every x∈A, we say that A is bounded above.

So my questions is that why is it important to state A⊂S

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# About least upper bound and ordered set

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads - least upper bound | Date |
---|---|

B Doubt regarding least upper bound? | Mar 2, 2016 |

About definition of 'Bounded above' and 'Least Upper Bound Property' | Mar 16, 2012 |

Greatest lower bound/least upper bound in Q | Nov 11, 2011 |

Least upper bound axiom | Jan 5, 2010 |

Question from a theorem in Baby Rudin (Re: Least-Upper-Bound Property) | Aug 9, 2009 |

**Physics Forums - The Fusion of Science and Community**