In relation to set theory and given a set U, what does U* mean? I'm working on homework for a programming language theory class (section on types) and one of the questions asks for the size of U*. I don't need the answer, just some help on what U* means :)
What does the notation U* mean?
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$\begingroup$
elementary-set-theory
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3I believe that is the Kleene star: http://en.wikipedia.org/wiki/Kleene_star. – 2012-09-18
1 Answers
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It means a set including every countable $U$
as a example define:
$U=\{a,b\}$
so we have:
$U^0 = \{\} = \lambda $
$U^1 = \{a,b\} = \lambda $
$U^2 = \{aa,ab,ba,bb\} = \lambda $
. . .
$U^* = \{U^0,U^1,U^2,U^3,... \}$
$U^+ = \{U^1,U^2,U^3,U^4,... \}$
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0@Henning Makholm: I meant empty a set without element do not care with notation this was why I put a equal $\lambda$ at the end of that anyway thank for notification – 2012-09-18