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Two's complement is the most common method of representing signed (positive, negative, and zero) integers on computers, [1] and more generally, fixed point binary values. Two's complement uses the binary digit with the greatest value as the sign to indicate whether the binary number is positive or negative; when the most significant bit is 1 the number is signed as negative and when the most ...
Cantor's diagonal argument (among various similar names [ note 1]) is a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbers – informally, that there are sets which in some sense contain more elements than there are positive integers.
All instances of log (x) without a subscript base should be interpreted as a natural logarithm, also commonly written as ln (x) or loge(x). In mathematics, the prime number theorem ( PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as ...
There are 92 elements containing the digits 1, 2, and 3 only, which John Conway named after the 92 naturally-occurring chemical elements up to uranium, calling the sequence audioactive. There are also two "transuranic" elements (Np and Pu) for each digit other than 1, 2, and 3. [5] [6] Below is a table of all such elements:
Composition (combinatorics) In mathematics, a composition of an integer n is a way of writing n as the sum of a sequence of (strictly) positive integers. Two sequences that differ in the order of their terms define different compositions of their sum, while they are considered to define the same integer partition of that number.
A prime number is a natural number greater than 1 with no divisors other than 1 and itself. According to Euclid's theorem there are infinitely many prime numbers, so there is no largest prime. Many of the largest known primes are Mersenne primes , numbers that are one less than a power of two, because they can utilize a specialized primality ...
Aleph-one. ℵ 1 is, by definition, the cardinality of the set of all countable ordinal numbers. This set is denoted by ω 1 (or sometimes Ω). The set ω 1 is itself an ordinal number larger than all countable ones, so it is an uncountable set. Therefore, ℵ 1 is distinct from ℵ 0. The definition of ℵ 1 implies (in ZF, Zermelo–Fraenkel ...
More than three decades later, Ice’s words ring out louder than ever, with one big difference. The outsiders are now insiders; once considered fringe subcultures, these working-class, story ...