real property: see property.

real number: see number.

real estate: see property.

Real Presence, expression of the belief among certain Christians, especially Roman Catholics and some Anglicans, that the actual presence of the body and blood of Jesus is in the Eucharist. Saints Ignatius of Antioch, Justin Martyr, and Irenaeus wrote of the bread and wine of the Eucharist as the actual body and blood of Christ. In the 4th cent. the focus shifted to the substantial transformation of the elements; by the 7th cent. the idea that the bread and wine were transmuted or converted in substance to the body and blood of Christ was prevalent throughout Christendom. This transformation was the subject of controversy in the 9th and 11th cent., and a Roman Council of 1079 issued a statement declaring that the bread and wine are changed substantially through consecration. The Fourth Lateran Council (1215) again sanctioned belief in transubstantiation. The doctrine recieved its classic formulation in the writing of St. Thomas Aquinas. The Council of Trent, confronted with Protestant challenges, especially from Ulrich Zwingli and John Calvin, issued an authoritative teaching upholding the doctrine of transubstantiation. For Protestant interpretations, see Lord's Supper.

Corte Real or Corte-Real, Gaspar, c.1450-1501?, Portuguese explorer. Sent by King Manuel I to search for the Northwest Passage, he is said to have discovered Greenland in 1500 and may have touched on the North American coast. He made a second voyage with his brother Miguel in 1501. He then sent Miguel home and continued his exploration, sailing southwest along the present U.S. coast. Gaspar Corte Real was lost. In 1502 Miguel Corte Real went in search of him but was also lost. The brothers certainly reached Newfoundland and made sweeping discoveries, but the results were inconclusive.

Ciudad Real, city (1990 pop. 58,170), capital of Ciudad Real prov., central Spain, in Castile-La Mancha, on a fertile plain between the Jabalón and Guadiana rivers. It is an agricultural marketplace, with farm-related industries. Ciudad Real was founded by Alfonso X of Castile in the 13th cent.; during the Peninsular War, the French defeated (1809) the Spanish in a battle nearby. The city preserves some of its medieval flavor; it has several notable Gothic churches.

Camino Real, El [Span.,=The Royal Road]. There are Camino Reals in most former Spanish possessions, including four in former Spanish territory in the United States. Probably the best-known American trail of this name, also called the Mission Trail, leads north from San Diego to San Francisco and beyond, running some 530 mi (853 km). The name is most commonly applied to the part of the trail north of Los Angeles. El Camino Real connected California's Franciscan missions and ran through such settlements as Santa Barbara, San Luis Obispo, San Juan Capistrano, Carmel, and Sonoma. The missions were mainly founded by two priests, Fr. Junípero Serra and his successor, Fr. Fermín Lasuén, in the period from 1769 to 1803. Together they established 18 of the 21 missions, many of them still extant and some extensively renovated, that flourished until the Mexican government ordered their secularization in 1833. Today, the surviving mission churches are houses of worship, tourist attractions, and icons of Spanish-American architecture. Route 101 follows much of the the old trail's route. The name El Camino Real also designates the 700 mi (1,100 km) New Mexican trail that was pioneered by Juan de Oñate in 1598 and formed the lifeline of Spain's New Mexican colony.

Alcalá la Real, town (1990 pop. 21,128), Jaén prov., S Spain, in Andalusia. It has well-known mineral springs. The town played an important part in the conquest of Granada from the Moors (15th cent.). In 1810 it was the site of a French victory in the Peninsular War.

Basic types of property in English common law, roughly corresponding to the division between immovables and movables in civil law. Real property consists of land, buildings, crops, and other resources, improvements, or fixtures still attached to the land. Personal property is essentially all property other than real property, including goods, animals, money, and vehicles.

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In mathematics, a quantity that can be expressed as a finite or infinite decimal expansion. The counting numbers, integers, rational numbers, and irrational numbers are all real numbers. Real numbers are used in measuring continuously varying quantities (e.g., size, time), in contrast to measurements that result from counting. The word real distinguishes them from the imaginary numbers.

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In property law, an agreement acknowledged in a deed or lease that restricts the free use or occupancy of property, such as by forbidding commercial use or certain types of structures. The restrictive covenant is as old as the law of property, being well-established in Roman law. The term is also used in business law to refer to an agreement whereby one party promises not to engage in the same business or a similar business in a particular area for a period of time.

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