My Math Forum Transforming relative values

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 February 6th, 2017, 05:54 AM #1 Newbie   Joined: Oct 2016 From: Croatia Posts: 5 Thanks: 0 Transforming relative values Hi, I am in a bit of a problem. What I have are two sets of numbers $\displaystyle X= \{x_i : x_i = \frac{1}{i} \mbox{ for } i\in [1..\inf)\}$ and $\displaystyle Y= \{y_i : y_i = \frac{1}{i!} \mbox{ for } i\in [1..\inf)\}$ obviously there is 1-to-1 mapping between them. What i need is to prove it. Any pointers?? Next I know that these are two different sets and the ! is a function connecting them. Given that one is interested in a pairwise distance between elements of two sets: $\displaystyle d(x_i,y_i) = | x_i - y_i |$ is there any chance to make any transformation in order to make these distances as small as possible. Am I making any sense?
 February 8th, 2017, 09:49 PM #2 Banned Camp   Joined: Dec 2012 Posts: 1,028 Thanks: 24 Transform it in a set theory problem, than apply the transfinite law of induction. {1,1!} ; {2,2!};....{i, i!}, {i+1, ?}

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