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Jun 13, 2011 at 2:52 comment added Yemon Choi While I agree that the question is not really suited to MO, I would at least offer some encouragement: this kind of question is both natural and good when one is trying to get to grips with notions of `size' for infinite subsets of the natural numbers. Hopefully the wikipedia link in Francesco Polizzi's comment may be of use.
Jun 13, 2011 at 2:37 history closed Todd Trimble
Andrés E. Caicedo
Harald Hanche-Olsen
gowers
Simon Thomas
off topic
Jun 12, 2011 at 19:13 answer added Richard Rast timeline score: 2
Jun 12, 2011 at 13:47 comment added Todd Trimble I hate to say it, but I feel obliged to: this site is for mathematics approximately at a research level. Please read the faq for appropriate places to ask this type of question.
Jun 12, 2011 at 12:33 comment added Francesco Polizzi The word "measure" in this context is not the appropriate one. You are probably looking for subsets of the naturals having zero density, even if your definition is not the correct definition of density. In fact, you should divide the counting measure by the size of $X_i$ before taking the $\liminf$ (or the $\limsup$). See en.wikipedia.org/wiki/Natural_density for more details.
Jun 12, 2011 at 12:09 history asked embarrasedtoask CC BY-SA 3.0