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Infinite Sets 2.5

Infinite Sets 2.5. Infinite Sets. א 0. N = {1,2,3,4, . . ., n , . . . }. n(N) =. Which set has more elements N or E?. N = {1,2,3,4, . . ., n , . . . } E = {2,4,6,8, . . .,2 n , . . . }. n(N) = n(E) = א 0. Therefore, the two sets are said to be equivalent. Exercises.

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Infinite Sets 2.5

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  1. Infinite Sets2.5

  2. Infinite Sets א0 N = {1,2,3,4, . . .,n, . . . } n(N)= Which set has more elements N or E? N = {1,2,3,4, . . .,n, . . . } E = {2,4,6,8, . . .,2n, . . . } n(N)= n(E) = א0 Therefore, the two sets are said to be equivalent.

  3. Exercises • Show that the two sets are equivalent by establishing a one-to-one correspondence. • O = the set of odd counting numbers • E = the set of even counting numbers • W = {0,1,2,3, . . .,n – 1, . . . } • N = {1,2,3,4, . . .,n, . . . }

  4. Exercises Show that the following set is infinite. 18. {5,10,15,20, . . . , 5n, . . . } {10,15,20,25, . . . , 5n + 5, . . . } The set is infinite since it is equivalent to one of its proper subsets.

  5. Exercises • Given , A = {15,23,31,39, . . .} and B = {1,2,3,4, . . .}, are equivalent, find • the element in A that corresponds to xεB. • the element in B that corresponds to 783εA. • 8x +7 b. 8x+7 = 783 • 8x=783-7 • 8x=776 • x=776/8 • x=97

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