What is the cardinal number of the following set

Question

B=(107,109,111,...,307)

Answer 1

One way....

Set up a counting relationship between element and element index (n):

107 is element 1

109 is element 2

111 is element 3

...

107 + 2(n-1) = element number n

Last element is 307: 107 + 2(n-1) = 307

2(n-1) = 200

2n = 202

n = 101

Therefore 307 is the 101^st element, and that is the cardinal number of the set.

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Another approach (this is not always easy to do, but for this set it works): manipulate the set contents into one that results in a set {1,2, ..., n}, then the cardinality is simply the last element's value:

{ 107, 109, 111, ..., 307 }

{ 0, 2, 4, ..., 200 } <<< subtracted 107 from each element

{ 0, 1, 2, ..., 100 } <<< divided each element by 2

{ 1, 2, 3, ..., 101 } <<< added 1 to each element

Clearly, 101 elements.