Hello there.(adsbygoogle = window.adsbygoogle || []).push({});

I understand (to the best of my ability) the Least Upper Bound property and the Nested Interval property, but I don't see how the two are equivalent properties.

LUB:

If [tex]S \subset \mathbb{R} [/tex] has an upper bound, then [tex]S[/tex] has a LUB

Nested Intervals:

If [tex]I_1 \supset I_2 \supset \cdots \supset I_n \supset \cdots[/tex] is a sequence of nested, closed, bounded, non-empty intervals, then

[tex]\bigcap_{n=1}^{\infty}I_n \neq \emptyset[/tex]

and length([tex]I_n \rightarrow 0[/tex], then [tex]\exists[/tex]

[tex]x_o \in \bigcap_{n=1}^{\infty}I_n[/tex]

(ie: a unique point exists in all the intervals)

Thanks in advance for clarifying this for me.

dogma

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

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

# LUB and Nested Interval Equivalancy

Loading...

Similar Threads - Nested Interval Equivalancy | Date |
---|---|

Continued fractions and nested radicals | Sep 23, 2008 |

Infinite number of open intervals | Feb 1, 2006 |

A formula of prime numbers for interval (q; (q+1)^2) | Sep 21, 2005 |

Piece-wise continuous functions on the close interval | Aug 8, 2005 |

A formula of prime numbers for interval (q; (q+1)^2), where q is prime number. | Jul 21, 2005 |

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