Infinity

Infinity (symbol: ∞) is an abstract concept describing something without any bound and is relevant in a number of fields, predominantly mathematics and physics. In mathematics, "infinity" is often treated as if it were a number (i.e., it counts or measures things: "an infinite number of terms") but it is not the same sort of number as natural or real numbers.

Georg Cantor formalized many ideas related to infinity and infinite sets during the late 19th and early 20th centuries. In the theory he developed, there are infinite sets of different sizes (called cardinalities). For example, the set of integers is countably infinite, while the infinite set of real numbers is uncountable.

History

Ancient cultures had various ideas about the nature of infinity. The ancient Indians and Greeks did not define infinity in precise formalism as does modern mathematics, and instead approached infinity as a philosophical concept.

Early Greek

The earliest recorded idea of infinity comes from Anaximander, a pre-Socratic Greek philosopher who lived in Miletus. He used the word apeiron which means infinite or limitless. However, the earliest attestable accounts of mathematical infinity come from Zeno of Elea (c. 490 BCE? – c. 430 BCE?), a pre-Socratic Greek philosopher of southern Italy and member of the Eleatic School founded by Parmenides. Aristotle called him the inventor of the dialectic. He is best known for his paradoxes, described by Bertrand Russell as "immeasurably subtle and profound".

Travel

Travel is the movement of people between relatively distant geographical locations, and can involve travel by foot, bicycle, automobile, train, boat, airplane, or other means, with or without luggage, and can be one way or round trip. Travel can also include relatively short stays between successive movements.

Etymology

The origin of the word "travel" is most likely lost to history. The term "travel" may originate from the Old French word travail. According to the Merriam Webster dictionary, the first known use of the word travel was in the 14th century. It also states that the word comes from Middle English travailen, travelen (which means to torment, labor, strive, journey) and earlier from Old French travailler (which means to work strenuously, toil). In English we still occasionally use the words travail and travails, which mean struggle. According to Simon Winchester in his book The Best Travelers' Tales (2004), the words travel and travail both share an even more ancient root: a Roman instrument of torture called the tripalium (in Latin it means "three stakes", as in to impale). This link reflects the extreme difficulty of travel in ancient times. Also note the torturous connotation of the word "travailler." Today, travel may or may not be much easier depending upon the destination you choose (i.e., Mt. Everest, the Amazon rainforest), how you plan to get there (tour bus, cruise ship, or oxcart), and whether or not you decide to "rough it (see extreme tourism and adventure travel). "There's a big difference between simply being a tourist and being a true world traveler," notes travel writer Michael Kasum. This is, however, a contested distinction as academic work on the cultures and sociology of travel has noted.