I am learning mathematics on my own, self-study type. Currently following Zakon's first book in his 3 part series.(adsbygoogle = window.adsbygoogle || []).push({});

In chapter 2, section 6, I have been successfully able to solve all the problem till I encountered 11'. It seems simple enough, but I am unable to understand the problem in the first place. I believe, Once I understand the problem itself, I will be in a position to chalk out a solution.

Please help me out in actually understanding the problem.

Here is the problem:

Chapter 2, Section 6, Problem 11’

11. Show by induction that each natural element x of an ordered field F can be uniquely represented as X=n ∙1', where n is a natural number in E^{1}(n ∈N) and 1' is the unity in F; that is, x is the sum of n unities.

Conversely, show that each such n ∙1' is a natural element of F.

Finally, show that, for m,n ∈N, we have

m<n iff mx<nx, provided x>0

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# Zakon : What is the problem?

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