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11 (number)

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11 (number)

11 (eleven) is the natural number following 10 and preceding 12. It is the smallest number whose name has three syllables.

"Eleven" derives from the Old English ęndleofon, which is first attested in Bede's late 9th-century Ecclesiastical History of the English People. It has cognates in every Germanic language (for example, German elf), whose Proto-Germanic ancestor has been reconstructed as *ainalifa-, from the prefix *aina- (adjectival "one") and suffix *-lifa-, of uncertain meaning. It is sometimes compared with the Lithuanian vienúolika, though -lika is used as the suffix for all numbers from 11 to 19.

The Old English form has closer cognates in Old Frisian, Saxon, and Norse, whose ancestor has been reconstructed as *ainlifun. This was formerly thought to be derived from Proto-Germanic *tehun ("ten"); it is now sometimes connected with *leikʷ- or *leip- ("left; remaining"), with the implicit meaning that "one is left" after counting to ten.

11 is a prime number, and a super-prime. 11 forms a twin prime with 13, and sexy pair with 5 and 17. 11 is also the first prime exponent that does not yield a Mersenne prime. 11 is part of a pair of Brown numbers. Only three such pairs of numbers are known. Rows in Pascal's triangle can be seen as representation of powers of 11.

An 11-sided polygon is called a hendecagon, or undecagon. A regular hendecagon is the polygon with the fewest number of sides that is not able to be constructed with a straightedge, compass, and angle trisector.

The Mathieu group is the smallest of twenty-six sporadic groups. It has order , with 11 as its largest prime factor. is the maximal subgroup Mathieu group , where 11 is also its largest prime factor.[citation needed]

The interval of an octave plus a fourth is an 11th. A complete 11th chord has almost every note of a diatonic scale.

In the mockumentary film This Is Spinal Tap, the idiomatic phrase up to eleven is coined to allude to going beyond the limitations of a system, in this case music amplifier volume levels.

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