Tell me more ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
up vote 1 down vote favorite
1

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 :)

share|improve this question
3  
I believe that is the Kleene star: en.wikipedia.org/wiki/Kleene_star. – Tarnation Sep 18 '12 at 2:45

1 Answer

up vote 0 down vote accepted

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 $

. . .

$U^* = \{U^0,U^1,U^2,U^3,... \}$

$U^+ = \{U^1,U^2,U^3,U^4,... \}$

share|improve this answer
a) $U^0$ is $\{\varepsilon\}$, not $\{\}$. b) What do you mean by setting each of the $U^n$s equal to (the same) $\lambda$? c) In the two last equations, surely you mean $U^* = U^0\cup U^1\cup U^2\cdots$, rather than the set you write on the right? – Henning Makholm Sep 18 '12 at 10:34
@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 – Mohammad Rafiee Sep 18 '12 at 13:01

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.