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February 6th, 2017, 05:54 AM   #1
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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?
miki is offline  
 
February 8th, 2017, 09:49 PM   #2
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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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