I am reading Ethan D. Bloch's book: The Real Numbers and Real Analysis ...(adsbygoogle = window.adsbygoogle || []).push({});

I am currently focused on Chapter 1: Construction of the Real Numbers ...

I need help/clarification with an aspect of Theorem 1.2.10 ...

Theorem 1.2.10 reads as follows:

Towards the end (second last line) of the above proof by Bloch, we read the following:

" ... ... We now have a contradiction to the fact that no element such as ##a + 1## exists in ##G##. ... ... "

I do not understand this remark ... as above ##a + 1## has earlier been proved to belong to ##G## ..

Can someone explain the remark "We now have a contradiction to the fact that no element such as ##a + 1## exists in ##G##" in the context of the proof and explain just what is going on ... ...

Help will be much appreciated ...

Peter

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# I The Well-Ordering Principle for the Natural Numbers ...

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