set_theory_not_used.tex

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\section{Cardinality and equivalence}

\definition{}{
The number of elements in a set A is the \textbf{cardinality} of the set and is denoted by $\left| A\right|$ 
}

\definition{}{
If two sets A and B have the same cardinality, we say they are \textbf{equivalent} and write $A \sim B$
}

\example{
The B = \{Tesla, Frisker\} and C = \{Ford, Toyota\} are not comparable, nor are they equal, but they are equivalent, since $\left| B\right|$ = $\left| C\right|$.
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Is it possible for two set to be comparable but not equivalent? Explain why or why not.
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    %\item Tammy is ordering a pizza and has the choice of three crusts: pan, regular or hand-tossed. She can choose Alfredo, Marinara or Pesto sauce and can add either peppers, mushrooms or spinach  as a topping and has to choose between mozzarella and feta cheese. Let the set of available crusts be C, sauces be S, toppings be T and cheeses be H. If Tammy doesn't like mushrooms and doesn't like feta cheese, how would you use set builder notation to represent the different pizzas she could order? 
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