- #1

Math Amateur

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MHB

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I am reading Micheal Searcoid's book: "Elements of Abstract Analysis" ... ...

I am currently focused on understanding Chapter 1: Sets ... and in particular Section 1.3 Ordered Sets ...

I need some help in fully understanding some remarks by Searcoid following Definition 1.3.10 ...

Definition 1.3.10 and the remarks following read as follows:

View attachment 8427

View attachment 8428In Searcoid's remarks following Definition 1.3.10 we read the following ...

"... ... every well ordered set is totally ordered ... ... Can someone please help me to prove that every well ordered set is totally ordered ... ...Help will be appreciated ...

Peter

=======================================================================

It may help MHB memebers reading the above post to have access to Definition 1.3.4 ... so I am providing access to the same ... as follows ...

View attachment 8429

Hope that helps ...

Peter

I am currently focused on understanding Chapter 1: Sets ... and in particular Section 1.3 Ordered Sets ...

I need some help in fully understanding some remarks by Searcoid following Definition 1.3.10 ...

Definition 1.3.10 and the remarks following read as follows:

View attachment 8427

View attachment 8428In Searcoid's remarks following Definition 1.3.10 we read the following ...

"... ... every well ordered set is totally ordered ... ... Can someone please help me to prove that every well ordered set is totally ordered ... ...Help will be appreciated ...

Peter

=======================================================================

It may help MHB memebers reading the above post to have access to Definition 1.3.4 ... so I am providing access to the same ... as follows ...

View attachment 8429

Hope that helps ...

Peter