Definition. Suppose that A and B are two sets with order relations [tex]<_A[/tex] and [tex]<_B[/tex] respectively. Define an order relation < on A x B by defining [tex]a_1 \ x \ b_1 < a_2 \ x \ b_2 [/tex] if [tex] a_1 <_A a_2 [/tex], or if [tex] a_1 = a_2[/tex] and [tex] b_1 <_B b_2[/tex]. It is called the(adsbygoogle = window.adsbygoogle || []).push({}); dictionary order relationon A X B.

OK. I think I am just confused by the syntax here. Up to this point Munkres has used (a , b) to denote an element of A x B. I think here he wants [tex] a_1 \ x \ b_1 [/tex] to be what I am used to being [tex] (a_1 , b_1 ) [/tex]

I think possibly the reason he changed notation, is that in an order relation (a , b) = { x| a < x < b} and he doesn't want us to get confused.

I just need verification.

What do you think?

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# Cartesian Product syntax in dictionary order relation definition

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