indicates that the letter so modified is indeed a glottal stop, not a long vowel. A second type of hamza, () whose diacritic is normally omitted outside of sacred texts, occurs only as the initial letter of the definite article and in some related cases. It differs from in that it is elided after a preceding vowel. Alif is always the carrier. Alif maddah: The is a double alif, expressing both a glottal stop and a long vowel. Essentially, it is the same as a sequence: (final ) , for example in 'last'. "It has become standard for a hamza followed by a long ā to be written as two alifs, one vertical and one horizontal." (the "horizontal" alif being the maddah sign). Alif maqṣūrah: The ى ('limited/restricted alif', ), commonly known in Egypt as (, 'flexible alif'), may appear only at the end of a word. Although it looks different from a regular alif, it represents the same sound , often realized as a short vowel. When it is written, is indistinguishable from final Persian ye or Arabic as it is written in Egypt, Sudan and sometimes elsewhere. The letter is transliterated as in Kazakh, representing the vowel /ə/. is transliterated as in ALA-LC, in DIN 31635, in ISO 233-2, and in ISO 233. In Arabic, alif maqsurah is not used initially or medially, and it is not joinable initially or medially in any font. However, the letter is used initially and medially in the Uyghur Arabic alphabet and the Arabic-based Kyrgyz alphabet, representing the vowel /ɯ/: (). Numeral As a numeral, alif stands for the number one. It may be modified as follows to represent other numbers. Other uses Mathematics In set theory, the Hebrew aleph glyph is used as the symbol to denote the aleph numbers, which represent the cardinality of infinite sets. This notation was introduced by mathematician Georg Cantor. In older mathematics books, the letter aleph is often printed upside down by accident, partly because a Monotype matrix for aleph was mistakenly constructed the wrong way up. Character encodings See also ʾ Al- Aleph number Arabic yāʼ "The Aleph", a short story by Jorge Luis Borges describing a point in space that contains all other spaces at once Hamzah Aleph (novel) Aleph null References Phoenician alphabet Alef Hebrew letters Vowel letters