Quandaries and Queries


If A=(1,2,3,4,...) and B=(5,10,15,20,...), is A equivalent to B. Why or Why not ?



By equivalent I expect that you are asking if there is a "one-to-ne relationship" between the sets or a "perfect matching" between the sets. I see a matchng between the sets in this way.

1 <------> 5
2 <------> 10
3 <------> 15
4 <------> 20
. <------> .
. <------> .

Thus every positive integer n on the left is paired with the 5 times n on the right. Also if you have a number on the right it is a multiple of 5, that is if m is on the right then there is a positive integer k so that m = 5 k and thus m, on the right is matched with k on the left.



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