**READING: II §3 LUB1**
Back to reading**:**
II §3 Preliminary

*begin quote ita***"**

*CHAPTER II* [:]
**
The Real Number System
**

Please get the book and read along. topic index contents

*
begin quote
ita-2-3-10-pg26
*
**"**

For any real number *x*, there is an integer *n*, such that *n**x*.

**"***end quote*

It seems to me that we already know from defining the natural numbers that there are arbitrarily large integers. Therefore, "existence of arbitrarily large integers" seems to be not precisely what is being asserted here. Hence the down arrow above replaces the statement of title that is usually present at the top of these pages.

Also (8 May 2012):

REFERENCE: ** A Primer of Infinitesimal Analysis**, by J. L. Bell, Cambridge University Press, 1998. Hereafter: Bell_APoIA. This book is based on the mathematical subject of category theory - which now also has been added to my list for future study along with non-standard analysis.

As I was reading Bell_APoIA for application to my studies in classical tensor analysis, I learned (page 106) that

on to §3: LUB 2