**READING: II §3 LUB4**
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II §3 LUB3

*begin quote ita***"**

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

Please get the book and read along. topic index contents

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

For any *x* and positive integer *N*, there is an integer *n* such that *x* **.**

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See the added details following Rosenlicht's proof**:**

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

To show this we merely have to apply LUB 3 to the number *Nx*, getting an integer *n*, such that *n**Nx**n*+1 **.**

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To get the desired result, we multiply all terms in *n**Nx**n*+1 by 1/*N***.** This is valid for the equality by F4. For the inequalities, we first use O7 to show that 1/*N* is greater than zero. Then use O4 twice - once for each inequality.

on to §3: LUB 5