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# L21_Fri_Mar_05_filled - MAE3811Sp 2010 Mahoney1 Sorry youre...

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1 MAE3811–Sp. 2010 Mahoney–1 Sorry you’re here the Friday before Spring Break… I know… I’m such a downer! Math Teachers/Tutors/Disciples of the Science of Patterns need or rather should know at least a little more math than the level they teach because… some stuff is just named/done so that it just won’t make sense till later, And If you know the road ahead you can ease the transition. Furthermore, if you know that teachers ahead of you are going to need your current students to really be grounded on something then you know what needs to be solid right now. Remember that… MAE3811–Sp. 2010 Mahoney–2 The most formal version of the Integers Each integer can be defined as the special diagonal subset of the Cartesian product above. Notice that there are two copies or clones of both the _________ numbers as well as the __________ numbers in the integers.

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2 MAE3811–Sp. 2010 Mahoney–3 Multiple Representations! As we talked about a little last time. Math geeks use what is called an equivalence relation, a generalization of the idea of equality, to establish that all the ordered pairs of those diagonals are equal in some sense and not equal to the other ordered pairs in the same sense. We’ve seen this before, Remember two sets were Equivalent if there was a one-to- one ________________ between them. That was an equivalence relation. (…if you know the road ahead…) The formal equivalence relation on the Cartesian Product of Whole numbers that
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L21_Fri_Mar_05_filled - MAE3811Sp 2010 Mahoney1 Sorry youre...

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