for differentiation). Set complement: is the complement of the set (other notation also exists). The negation of an event in probability theory: (other notation also exists). The result of a transformation: The transpose of a matrix (other notation also exists) The dual of a vector space The prime is said to "decorate" the letter to which it applies. The same convention is adopted in functional programming, particularly in Haskell. In geometry, geography and astronomy, prime and double prime are used as abbreviations for minute and second of arc (and thus latitude, longitude, elevation and right ascension). In physics, the prime is used to denote variables after an event. For example, would indicate the velocity of object A after an event. It is also commonly used in relativity: the event at in frame , has coordinates in frame . In chemistry, it is used to distinguish between different functional groups connected to an atom in a molecule, such as and , representing different alkyl groups in an organic compound. The carbonyl carbon in proteins is denoted as , which distinguishes it from the other backbone carbon, the alpha carbon, which is denoted as . In physical chemistry, it is used to distinguish between the lower state and the upper state of a quantum number during a transition. For example, denotes the upper state of the quantum number while denotes the lower state of the quantum number . In molecular biology, the prime is used to denote the positions of carbon on a ring of deoxyribose or ribose. The prime distinguishes places on these two chemicals, rather than places on other parts of DNA or RNA, like phosphate groups or nucleic acids. Thus, when indicating the direction of movement of an enzyme along a string of DNA, biologists will say that it moves from the end to the end, because these carbons are on the ends of the DNA molecule. The chemistry of this reaction demands that the be extended by DNA synthesis. Prime can also be used to indicate which position a molecule has attached to, such as Use in linguistics The prime can be used in the transliteration of some languages, such as Slavic languages, to denote palatalization. Prime and double prime are used to transliterate Cyrillic yeri (the soft sign, ь) and yer (the hard sign, ъ). However, in ISO 9, the corresponding modifier letters are used instead. Originally,