# Inductive Definition on the set of strings

Given:

$$\Sigma = \{ a, b, c \}.$$

I am trying to give the inductive definitions of both the set of strings $\Sigma^*$ and $\Sigma^+$.

Thank you.

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And what is the 'set of strings $\sigma^*$' and what is the 'set of strings $\sigma^+$' ? And more imporatntly, what is your question? This isn't facebook, you don't need to give us a status update to let us know what you are doing. –  Arturo Magidin Mar 24 '11 at 18:02
Sigma* and Sigma+ aren't given. The question is what are the inductive definitions of both Sigma* and Sigma+. I now realise the wording of the question is suspect and I apologise. –  Garee Mar 24 '11 at 18:07
There must be a definition of what it means, in general, to have "sigma*" and "sigma+". Otherwise, they are just words with no meaning, and you cannot give a definition, inductive or otherwise, for words with no meaning. –  Arturo Magidin Mar 24 '11 at 18:08

The set $\Sigma^*$ contains all strings. The set $\Sigma^+$ contains all non-empty strings.
Your inductive definition of $\Sigma^*$ will go like this: a string is either empty or of the form $sa$ where $s$ is a string and $a$ is a character. So to form a string, you start with the empty string and keep adding characters at the end.