Eleven

Eleven
	11
presentation
Roman	XI
dual	1011
Octal	13
Duodecimal	B.
Hexadecimal	B.
Morse code	- - - - - - - -
Chinese	十一
Mathematical properties
sign	positive
parity	odd
Factorization	Prime number
Divider	1, 11

The eleven (11) is the natural number between ten and twelve . It is odd and a prime number .

Linguistic

The number word eleven , even to the 19th century eleven , comes from the Old High German word einlif from, made from the roots of a (one) and lif (left) (see. English "left"). So it means roughly “remainder one”. It describes the rest that remains when you have counted ten out of eleven (with your fingers). There is a similar formation in Lithuanian : The numbers eleven to nineteen are formed with the ending -lika , which belongs to the family of the word lend - (over) let .

The Latin word undecim and the Greek ἕνδεκα (hendeka) can be found in foreign words such as Undezime , Undekasilan and Hendekasyllabus .

mathematics

11 is the smallest prime number p for which the Mersenne number is not prime, i.e. not a Mersenne prime number . . It is the smallest 2-digit prime number and the smallest 2-digit prime number palindrome in the decimal system. But the 11 is not a palindromic number according to a stricter definition (see Strictly non-palindromic number ). ${\ displaystyle M_ {p} = 2 ^ {p} -1}$ ${\ displaystyle 2 ^ {11} -1 = 2047 = 23 \ cdot 89}$

In the decimal system , the divisibility of a natural number by 11 is easy to test: Form the alternating cross sum of the number, i.e. add all digits in odd places and subtract all digits in even places (e.g. the alternating cross sum of 12345 is the same .) . The original number is divisible by 11 if and only if the alternating checksum is a multiple of 11 or 0. ${\ displaystyle 5-4 + 3-2 + 1 = 3}$

There is a second option where the number is divided by an integer by 100 and the remainder is added to it. The calculation rule must be applied to the respective result until it is less than 100. The number is divisible by 11 if the result is also a small multiple of 11 (11, 22, 33, 44, 55, 66, 77, 88, 99).

Example for 5489: and ${\ displaystyle 54 + 89 = 143}$ ${\ displaystyle 1 + 43 = 44}$

Similarly, it is also possible to divide the number as an integer by 10 and subtract the remainder. This is carried out until you have reached a single-digit result. If this is 0, the number is divisible by 11.

Example for 5489: , and (the number is divisible by so 11). The solution to the division can be read from the subtracted numbers by writing them down in reverse order and summarizing them as a number. In this example 499. This is easy to see, since in the example first 99, then 990 and finally 4400 are subtracted and thus a written division is carried out in the reverse order. Incidentally, this procedure leads directly to the formulation with the change sum, since with every second step a number reduced by the previous number is subtracted, i.e. the first can also be subtracted directly and the second added because . ${\ displaystyle 548-9 = 539}$ ${\ displaystyle 53-9 = 44}$ ${\ displaystyle 4-4 = 0}$ ${\ displaystyle c- (ba) = c-b + a}$

For every number it holds that at least one prime number exists, so that the product divides. ${\ displaystyle n> 11}$ ${\ displaystyle p> 11}$ ${\ displaystyle p}$ ${\ displaystyle n \ cdot (n + 1) \ cdot (n + 2) \ cdot (n + 3)}$

The number 11 is also a Størmer number .

In the Roman numerals , XI corresponds to eleven.

Natural sciences

In the periodic table of chemistry, 11 is the atomic number of sodium .

History and society

The eleven men in ancient Athens oversaw the prison system and monitored the execution of the death penalty .

Penalty advice
In the 19th century the eleven became the number of the Rhenish carnival . The ceremonial meetings are presided over by a councilor, the beginning of the carnival is recently celebrated on November 11th at 11:11 am. This is said to have derived from the abbreviated motto of the French Revolution “Égalité, Liberté, Fraternité” . However, it may also be a parody of often ten or twelve-member boards.
The eleven is the smallest number of schnapps .
Paragraph 11 : "We continue to drink!"
The eleventh commandment : "You shouldn't get caught!"
911 out! is the name of a popular card game for children.
The penalty kick in a football game comes from the dimensions of the pitch originally defined in Anglo-Saxon dimensions . It is exactly 10.9728 m, i.e. 12 yards . Football teams have consistently consisted of eleven players since 1870 , hence the synonym Elf for football team ( see also: Goldene Elf ).
11 can also symbolically stand for the Islamic expression Allahu Akbar ( God is great ).
The number 11 on the back is the number of the left winger / striker in football.
The Swiss city of Solothurn has many historical references to the number eleven, which is why it is regionally referred to as the Solothurn number .

Culture and economy

Elf Sons is a story by Franz Kafka .
Eleven Minutes (Onze Minutos) is a novel by Paulo Coelho .
Elf , character from the Netflix series Stranger Things
The Association of XI in Berlin and The Elf in Munich were two important groups of visual artists at the end of the 19th century and forerunners of the Munich and Berlin Secession .
The Group 11 was a Stuttgart group of artists in the 1950s.
11er Haus : an Austrian television series from 2005
11er Nahrungsmittel : an Austrian manufacturer of french fries

Web links

Wiktionary: Elf - explanations of meanings, word origins, synonyms, translations

Wiktionary: elf - explanations of meanings, word origins, synonyms, translations

Individual evidence

↑ Where does the number 11 come from? on the website of Johannes Gutenberg University Mainz
^ The foolish elf in the carnival lexicon of the Südwestrundfunk

[1] Where does the number 11 come from? on the website of Johannes Gutenberg University Mainz

[2] The foolish elf in the carnival lexicon of the Südwestrundfunk