The number eleven is a fascinating mathematical object. It's the smallest two-digit prime number and the first repdigit greater than single digits. Eleven appears frequently in mathematics, from its unique divisibility rules to its role in number theory.
Eleven has a unique divisibility rule. To test if a number is divisible by eleven, we alternate between adding and subtracting its digits from right to left. For example, with 1331, we calculate 1 minus 3 plus 3 minus 1, which equals zero. Since zero is divisible by eleven, 1331 is also divisible by eleven.
Eleven can be represented in different number systems. In binary, it's 1011, which equals 8 plus 2 plus 1. In octal base 8, it's 13, and in hexadecimal, it's represented by the letter B. These different representations show the same quantity expressed in various mathematical bases.
Eleven has fascinating mathematical properties. It's a palindromic prime, reading the same forwards and backwards. Eleven and thirteen form a twin prime pair, differing by only two. It's also a repunit in base 10, and its powers create palindromic numbers like 121 and 1331.
Eleven appears throughout our daily lives. Football teams field eleven players, making it central to the world's most popular sport. In technology, eleven appears in binary systems and ISBN check digits. Even in popular culture, from Spinal Tap's amplifiers that 'go to eleven' to the mystical 11:11 wish time, this number connects mathematics to human experience.