- published: 29 May 2014
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11 (eleven i/ɨˈlɛvɨn/ or /iˈlɛvɛn/) is the natural number following 10 and preceding 12.
Eleven is the first number which cannot be counted with a human's ten fingers. In English, it is the smallest positive integer requiring three syllables and the largest prime number with a single-morpheme name. Its etymology originates from a Germanic compound ainlif meaning "one left".). It is also the second number in the "teens."
Eleven is the 5th smallest prime number. It is the smallest two-digit prime number in the decimal base; as well as, of course, in undecimal (where it is the smallest two-digit number). It is also the smallest three-digit prime in ternary, and the smallest four-digit prime in binary, but a single-digit prime in bases larger than eleven, such as duodecimal, hexadecimal, vigesimal and sexagesimal. 11 is the fourth Sophie Germain prime, the third safe prime, the fourth Lucas prime, the first repunit prime, and the second good prime. Although it is necessary for n to be prime for 2n − 1 to be a Mersenne prime, the converse is not true: 211 − 1 = 2047 which is 23 × 89. The next prime is 13, with which it comprises a twin prime. 11 is an Eisenstein prime with no imaginary part and real part of the form 3n − 1. Displayed on a calculator, 11 is a strobogrammatic prime and a dihedral prime because it reads the same whether the calculator is turned upside down or reflected on a mirror, or both.
A number is a mathematical object used to count and measure. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers.
Mathematical operations are certain procedures that take one or more numbers as input and produce a number as output. Unary operations take a single input number and produce a single output number. For example, the successor operation adds one to an integer, thus the successor of 4 is 5. Binary operations take two input numbers and produce a single output number. Examples of binary operations include addition, subtraction, multiplication, division, and exponentiation. The study of numerical operations is called arithmetic.
A notational symbol that represents a number is called a numeral. In addition to their use in counting and measuring, numerals are often used for labels (telephone numbers), for ordering (serial numbers), and for codes (e.g., ISBNs).