# What does the notation U* mean?

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 :)

It means a set including every countable $U$

as a example define:

$U=\{a,b\}$

so we have:

$U^0 = \{\} = \lambda$

$U^1 = \{a,b\} = \lambda$

$U^2 = \{aa,ab,ba,bb\} = \lambda$

. . .

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

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

• 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