403 articles
Atan2
Atan2, also called Arctan2, is the two-argument arctangent function returning the angle to a point (x, y) in [−π, +π], fixing the quadrant from both signs.
Babylonian cuneiform numerals
Babylonian cuneiform numerals are the base 60 place-value number system of ancient Mesopotamia, written with just two wedge signs into clay and surviving today in minutes and seconds.
Balanced ternary
Balanced ternary is a base-3 numeral system whose digits are −1, 0, and +1, so negative numbers need no separate sign; it drove the Soviet Setun computer of 1958.
Bell number
The Bell number B(n) is the number of ways to partition a set of n labeled elements into non-empty subsets; the sequence begins 1, 1, 2, 5, 15.
Bell numbers
The Bell numbers, named for mathematician Eric Temple Bell, count the partitions of a set of n labeled elements, beginning 1, 1, 2, 5, 15, 52.
Bernoulli number
The Bernoulli numbers are a sequence of rational numbers introduced by Jacob Bernoulli to sum powers of integers, appearing in the Euler–Maclaurin formula and the Riemann zeta function.
Bfloat16
Bfloat16 (Brain Floating Point, BF16) is a 16-bit floating-point format for machine learning, introduced by Google Brain on TPUs, with FP32's range but lower precision.
Billion
Billion, also called one billion, is the number 1,000,000,000 (a thousand million) in American and British English, though older European usage gives it the value 10^12.
Binary arithmetic
Binary arithmetic is arithmetic in base 2 using only the digits 0 and 1, the arithmetic of electronic computers, first described by Leibniz around 1679.
Binary logarithm
The binary logarithm, also called log2 or the base-2 logarithm, is the logarithm to base 2, the exponent y such that 2 to the power y equals x.
Binary number
A binary number, also called a base-2 number, is written using only the digits 0 and 1, and digital computers use it to store and manipulate all data.
Binary-coded decimal
Binary-coded decimal (BCD) is a way of representing decimal digits in digital systems, storing each digit 0 through 9 in its own 4-bit group of bits.
Binomial series
The binomial series, also known as Newton's binomial series, is the power series for (1+z)^α, converging for |z| < 1 and probably first stated by Newton in 1664–1665.
Bit numbering
Bit numbering assigns index numbers to the individual bits of a value. Conventions include LSB 0, where 0 is least significant, and MSB 0, where 0 is most significant.
Bitwise operation
A bitwise operation, also known as a bit operation, acts on the individual bits of binary numerals rather than on the numbers those bits represent, using operators like AND, OR, XOR, and shifts.
Bitwise operations in C
Bitwise operations in C manipulate individual bits of integer values with operators such as AND, OR, XOR, complement, and shifts, letting C work close to the hardware.
Blackboard bold
Blackboard bold, also called double-struck or chalkboard bold, is a mathematical typeface with doubled strokes imitating bold, used chiefly for number systems like ℤ, ℝ, and ℂ.
Booth's multiplication algorithm
Booth's multiplication algorithm, also known as Booth's algorithm, is a signed binary multiplication technique published by Andrew D. Booth in 1951 that handles two's complement numbers of either sign without separate correction.
Bose–Einstein statistics
Bose–Einstein statistics, also called the Bose–Einstein distribution, describes identical particles with integer spin (bosons), any number of which may occupy the same quantum state; Bose introduced it in 1924.
Cantor's diagonal argument
Cantor's diagonal argument, or diagonalization, is an 1891 proof by Georg Cantor that no list can contain every real number in [0,1], showing the reals are uncountable.
Cardinal arithmetic
Cardinal arithmetic is the arithmetic of cardinal numbers, the sizes of sets. For infinite cardinals, addition and multiplication collapse to the maximum, so the deep part is exponentiation.
Cardinal characteristic of the continuum
A cardinal characteristic of the continuum, also called a cardinal invariant, is a cardinal number, usually the minimal size of a set of reals with a given property, describing the structure of the real line.
Cardinality of the continuum
The cardinality of the continuum, also called the power of the continuum, is the size of the set of real numbers, strictly larger than that of the natural numbers.
Carry-lookahead adder
The carry-lookahead adder (CLA), also known as a fast adder, is a digital circuit that adds binary numbers by computing every carry in parallel instead of rippling, introduced in 1958.
Catalan number
The Catalan numbers, also called the Catalan sequence, form an integer sequence beginning 1, 1, 2, 5, 14, 42 that counts balanced parentheses and triangulations.
Catastrophic cancellation
Catastrophic cancellation is the loss of significant digits that occurs when two nearly equal numbers are subtracted, inherent to approximations rather than floating point itself, and fixed by algebraic rewriting.
Cavalieri's principle
Cavalieri's principle, also called the method of indivisibles, is a geometric rule stating that two solids of the same height with equal cross-sectional areas at every level have equal volumes.
Champernowne constant
The Champernowne constant, formed by writing the positive integers in order as 0.123456789101112..., is normal in base 10, proved by David Champernowne in 1933.
Cichoń's diagram
Cichoń's diagram, named after the Polish mathematician Jacek Cichoń, is a diagram in set theory displaying the ZFC-provable inequalities among ten cardinal characteristics of the continuum.
Cofinality
Cofinality, written cf(α), is a set theory concept measuring how hard an ordinal is to approach from below: the least order type of a cofinal subset of it.