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--- mathematics:languagesandgrammar [2024/10/09 14:51] – tami
+++ mathematics:languagesandgrammar [2024/10/09 15:12] (current) – [Closure of an alphabet] tami
@@ Line 34: / Line 34: @@
 $$
+==== Closure of an alphabet ====
+The closure of $\Sigma$ coincides with out definition of $\Sigma^{\ast}$ as the set f all string over $\Sigma$. In other words, we have a nice representation of $\Sigma^{\ast}$ as follows:
+$$
+  \Sigma^{\ast} = \Sigma^0 \cup \Sigma^1 \cup \Sigma^1 \cup ...
+$$
+Where $\Sigma^k$ denotes the set of strings of length $k$, each of whose symmbols in $\Sigma$.
 ===== Grammar =====