Proof Patterns by Mark Joshi

Author:Mark Joshi
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

This is clearly injective and the image sets are certainly cuts. For the construction to be useful, this map must not be onto. In other words, there needs to be cuts that are not of this form. An easy example is the one studied above, take to be the negative rationals together with such that

There is a natural ordering on the space of cuts. We simply say if and only if . We want to show that we now get the least upper bound property. Suppose we have a collection of cuts

with ranging over some index set . We can let

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.