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A city is a relatively large and permanent settlement. Although there is no agreement on how a city is distinguished from a town within general English language meanings, many cities have a particular administrative, legal, or historical status based on local law.
The City of London is a city within London. The City constituted most of London from its settlement by the Romans in the 1st century AD to the Middle Ages, but the conurbation has since grown far beyond its borders. It is widely referred to as the City (often written on maps as “City” and differentiated from the phrase “the city of London” by capitalising the word City) or the Square Mile as it is 1.12 sq mi (2.90 km2) in area

Source: Wikipedia (The City and City)