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November 8th, 2007, 09:38 AM  #1 
Newbie Joined: Oct 2007 From: Brazil Posts: 8 Thanks: 0  Cardinality of the set of sequences of non negative integers
Let S be the set of all sequences of nonnegative integers. What's the cardinality of S? I was told it equals the cardinality of the set of all functions from R to R that sends rationals into rationals, but couldn't prove this If, for each p >=2, we define S_p as the set of all sequences of nonnegative integers bounded by p, then each (a_1, a_2....a_n...) of S_p can be seen as the padic representation of the number 0.a1 a2...a_n..., so that to each element of S_p there corresponds one elemet of [0,1]. This proves the cardinalty of S_p, and therefore of S, is at least Aleph(1), but this conclusion is not very interesting. Does anyone have a hint? Thank youy 
November 8th, 2007, 10:52 AM  #2  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: ardinality of the set of sequences of non negative integ Quote:
 

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