---
title: "alphabet"
type: concept
related: [String, Alphabet]
source: https://www.jemoka.com/posts/kbhalphabet/
confidence: high
status: active
---

see also in programming string (C)
an alphabet \(\Sigma\) is a finite set a finite-sequence of elements in \(\Sigma\) is called a string the set of all strings in \(\Sigma\) is called \(\Sigma^{*}\), which includes the empty string for a particular string \(x\), the length of it is \(|x|\) the string of length zero is called \(\varepsilon\) a language is a subset of \(\Sigma^{*}\), meaning its a set of strings Omer seems to call strings &ldquo;words&rdquo; sometimes.
languages are boolean function over strings For every language \(L\) over \(\Sigma\) corresponds to a unique function \(f: \Sigma^{*} \to \{0,1\}\), whereby if \(f(x) = 1\), then \(x \in L\); otherwise, if \(f(x) = 0\), \(x \not \in L\).
