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L05_Fri_Jan_22 - MAE3811Sp 2010 Mahoney1 Last time we...

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1 MAE3811–Sp. 2010 Mahoney–1 Last time we talked about Arguments and Quantifiers… All Chihuahuas are dogs. Pepper is a Chihuahua. Therefore, Pepper is a dog. In the broad sense, the Formal logic we’ve just learned is considered to be a “Foundation of Mathematics” because you build other mathematical ideas from it. Another Foundation of Mathematics is Set theory. Set Theory can be considered an alternate version, almost like an alternate dialect, for logic. The Two fields are closely related and have a lot of parallel ideas. MAE3811–Sp. 2010 Mahoney–2 Imagine if we gathered all the dogs in the word and enclosed them with a big round fence. We call this collection of dogs the __________ of all dogs. Each Dog is a ____________ of this set. In general, a Set is a ____________ of ____________. Individual things in the set are called the sets’ _____________ or _____________. In symbols we often denote sets with ___________ __________. In the example above, we might call it the set _____.
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2 MAE3811–Sp. 2010 Mahoney–3 So here is our set of all dogs… Now my Chihuahua is in there and I don’t want here getting eaten or trampled by the bigger dogs, so I build another smaller fence inside the big fence and I put all the Chihuahua’s in here.
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