The free monoid on an alphabet consists of all finite words in its letters, including the empty word, under concatenation. Distinct words represent distinct elements.
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A **free monoid** is a mathematical structure that consists of a set of elements combined with an associative operation. More specifically, it is formed from a set and includes the operation of concatenation (or joining) of its elements. Here are the key details: 1. **Set**: Let \( S \) be a set of elements. For example, \( S \) could be a set of characters or symbols.