# Ordinals ... Searcoid, Theorem 1.4.6 ...

#### Peter

##### Well-known member
MHB Site Helper
I am reading Micheal Searcoid's book: "Elements of Abstract Analysis" ... ...

I am currently focused on understanding Chapter 1: Sets ... and in particular Section 1.4 Ordinals ...

I need some help in fully understanding Theorem 1.4.6 ...

My question regarding the above proof by Micheal Searcoid is as follows:

How do we know that $$\displaystyle \alpha$$ and $$\displaystyle \beta$$ are not disjoint? ... indeed ... can they be disjoint?

What happens to the proof if $$\displaystyle \alpha \cap \beta = \emptyset$$?

Help will be appreciated ...

Peter

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It may help MHB
readers of the above post to have access to the start of Searcoid's section on the ordinals ... so I am providing the same ... as follows:

Hope that helps ...

Peter

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