View source for Alphabet

A list (finite set) of letters (cf. [[Letter|Letter]]). An alphabet usually contains the letters which are required to develop a certain system of symbols or, as is sometimes said, a language. For two alphabets <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a012/a012020/a0120201.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a012/a012020/a0120202.png" />, their union <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a012/a012020/a0120203.png" />, their intersection <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a012/a012020/a0120204.png" />, their difference <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a012/a012020/a0120205.png" />, as well as the inclusion relation <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a012/a012020/a0120206.png" /> are defined in the obvious manner. For convenience, the concept of an empty alphabet, i.e. an alphabet without any letters, may also be considered.