Let x be a real number. show that there is m integer so that m <= x < m + 1. show that m is unique
Favorites|Homepage
Subscriptions | sitemap
HOME > > Let x be a real number. show that there is m integer so that m <= x < m + 1. show that m is unique

Let x be a real number. show that there is m integer so that m <= x < m + 1. show that m is unique

[From: ] [author: ] [Date: 12-08-13] [Hit: ]
2.Use the fact that any nonempty set of natural numbers has a least element.This is logically equivalent to good old induction.Theres a little bit of kludging from the fact that x could be negative, but thats not too hard to patch up.The rest is just details.......
The answer depends on the level at which you're studying the problem. I'll give hints assuming you're taking a fairly high-level course, but it may or may not be helpful to you:

There's a fairly straightforward path to a proof that you can get by combining these two ideas:

1. Represent x by its Dedekind cut, and consider the set of integers within that cut.

2. Use the fact that any nonempty set of natural numbers has a least element. This is logically equivalent to good old induction.

There's a little bit of kludging from the fact that x could be negative, but that's not too hard to patch up. The rest is just details.


If you're taking a more introductory-level class, I honestly don't know how you'd prove it without begging the question.
1
keywords: is,that,Let,unique,integer,so,real,show,there,number,1.,be,lt,Let x be a real number. show that there is m integer so that m <= x < m + 1. show that m is unique
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .