Unformatted text preview: M × W ; 3. products are analogous to the product types of Haskell: for instance, (Int, Char) is Haskell’s notation for the product Int × Char . Fact Let A and B be ±nite sets. Then  A × B  =  A  ×  B  . Proof If you are uncertain about whether this fact is true, explore examples such as { a,b } × { 1 , 2 , 3 } and ∅ × { a,b } . We give an informal proof, which you do not need to remember. Suppose that A and B are arbitrary sets with A = { a 1 ,...,a m } and B = { b 1 ,... ,b n } . Draw a table with m rows and n columns of the members of A × B : ( a 1 ,b 1 ) ( a 1 ,b 2 ) ... ( a 2 ,b 1 ) ( a 2 ,b 2 ) ... ... Such a table has m × n entries. ± We can extend this de±nition of Cartesian product to the nary case. D EFINITION 2.12 ( nARY PRODUCT ) 1. For any n ≥ 1 , an ntuple is a sequence ( a 1 ,... ,a n ) of n objects where the order of the a i matter. 12...
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This note was uploaded on 01/02/2010 for the course MATH Math2009 taught by Professor Koskesh during the Spring '09 term at SUNY Empire State.
 Spring '09
 Koskesh
 Math

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