ma2201a17exercises07.pdf

# ma2201a17exercises07.pdf - In lecture 7 we finished the...

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In lecture 7 we finished the material on lexicographic order, and Russel’s Paradox. In honor or Labor Day, there is just one problem. 1. Let A = { a, b, c, d, e } , B = { a,c,e,g,i } , and C = { d, e, f, g, h, i } . In this exer- cise, order the elements of the cartesian products lexicographically, using the alphabetical order on the individual sets. (We are always counting from 0.) a) Show that ( e, e, e ) is the 112’th element (ordinal 112) of A × B × B . b) What is the ordinal of ( e, e, e ) in A × B × A . c) What is the ordinal of ( e, e, e ) in B × A × B . d) What is the ordinal of ( e, e, e ) in A × B × C . e) What is the ordinal of ( e, e, e ) in C × B × A . f) What is the ordinal of ( e, e, e ) in C × B × C . g) What is the 100’th element in A × A × A . h) What is the 100’th element in B × B × B . i) What is the 100’th element in C × C × C . j) What is the 100’th element in A × B × C . k) What is the 100’th element in C × B × A . Don’t bother this problem Bat Masterson was playing poker with Doc Holliday and Wyatt Earp, and Masterson was complaining that his five cards were very bad.. Masterson said he had no aces and, in fact, no face-cards. “You might have
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• Spring '10
• PeterChristopher

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