Wolfram Research Mathworld, Repository hosted at UIUC
(13.662 recursos)
Wolfram Research's MathWorld is a comprehensive and interactive mathematics encyclopedia intended for students, educators, math enthusiasts, and researchers. It has been assembled by internet encyclopedist Eric W.ÊWeisstein with assistance from the mathematics and internet communities. Like the discipline of mathematics, this site is continuously updated to include new material and incorporate new discoveries. This is a free service for the mathematical community provided by Wolfram Research, makers of Mathematica, with additional support from the National Science Foundation.
Mostrando recursos 1 - 20 de 152
1.
Absolutely Normal -- from MathWorld - Weisstein, Eric W.
A real number that is b-normal for every base 2, 3, 4, ... is said to be absolutely normal. As proved by Borel (1922, p. 198), almost all real numbers in [0,1) are absolutely normal (Niven 1956, p. 103; Stoneham 1970; Kuipers and Niederreiter 1974, p. 71; Bailey and Crandall 2003). The first specific construction of an absolutely normal number was by Sierpinski (1917), with another method presented by Schmidt (1962). These results were both obtained by complex constructive devices (Stoneham...
2.
Addend -- from MathWorld - Weisstein, Eric W.
A quantity to be added to another, also called a summand. For example, in the expression a+b+c, a, b, and c are all addends. The first of several addends, or "the one to which the others are added" (a in the previous example), is sometimes called the augend. See also: Addition, Augend, Plus, Radicand
3.
Addition -- from MathWorld - Weisstein, Eric W.
The combining of two or more quantities using the plus operator. The individual numbers being combined are called addends, and the total is called the sum. The first of several addends, or "the one to which the others are added," is sometimes called the augend. The opposite of addition is subtraction. While the usual form of adding two n-digit integers (which consists of summing over the columns right to left and "carrying" a 1 to the next column if the sum exceeds 9)...
4.
Additively Closed -- from MathWorld - Weisstein, Eric W.
A mathematical object S is said to be additively closed if a,b \in S implies that a+b\in S. See also: Multiplicatively Closed
5.
Anomalous Cancellation -- from MathWorld - Weisstein, Eric W.
The simplification of a fraction a/b which gives a correct answer by "canceling" digits of a and b. There are only four such cases for numerator and denominators of two digits in base 10: 64/16=4/1=4, 98/49=8/4=2, 95/19=5/1=5, and 65/26=5/2 (Boas 1979). The concept of anomalous cancellation can be extended to arbitrary bases. prime bases have no solutions, but there is a solution corresponding to each proper divisor of a composite b. When b-1 is prime, this type of solution is the only...
6.
Archimedes' Axiom -- from MathWorld - Weisstein, Eric W.
An axiom actually attributed to Eudoxus (Boyer and Merzbach 1991, pp. 89-90) which states that {a\over b} = {c\over d} iff the appropriate one of following conditions is satisfied for integers m and n: 1. If ma < nb, then mc < nd. 2. If ma = nb, then mc = nd. 3. If ma > nb, then mc > nd. Also known as the continuity axiom or Archimedes' lemma, this axiom survives in the writings of Eudoxus (Boyer and Merzbach 1991). It states that, given two magnitudes having a ratio, one can find...
7.
Arithmetic -- from MathWorld - Weisstein, Eric W.
Arithmetic is the branch of mathematics dealing with integers or, more generally, numerical computation. Arithmetical operations include addition, congruence calculation, division, factorization, multiplication, power computation, root extraction, and subtraction. Arithmetic was part of the quadrivium taught in medieval universities. A mnemonic for the spelling of "arithmetic" is "a rat in the house may eat the ice cream." The branch of mathematics known as number theory is...
8.
Arnauld's Paradox -- from MathWorld - Weisstein, Eric W.
Arnauld's paradox states that if negative numbers exist, then (-1)/1 must equal 1/(-1), which asserts that the ratio of a smaller to a larger quantity equals the ratio of the same larger quantity to the same small quantity. See also: Negative
9.
Augend -- from MathWorld - Weisstein, Eric W.
The first of several addends, or "the one to which the others are added," is sometimes called the augend. Therefore, while a, b, and c are addends in a+b+c, a is the augend. See also: Addend, Addition
10.
Base -- from MathWorld - Weisstein, Eric W.
The word "base" in mathematics is used to refer to a particular mathematical object that is used as a building block. The most common uses are the related concepts of the the number system whose digits are used to represent numbers and the number system in which logarithms are defined. It can also be used to refer to the bottom edge or surface of a geometric figure. A real number x can be represented using any integer number b as a base (sometimes also called a radix or scale). The...
11.
Binary -- from MathWorld - Weisstein, Eric W.
The base 2 method of counting in which only the digits 0 and 1 are used. In this base, the number 1011 equals 1\cdot 2^0+1\cdot 2^1+0\cdot 2^2+1\cdot 2^3=11. This base is used in computers, since all numbers can be simply represented as a string of electrically pulsed ons and offs. In computer parlance, one binary digit is called a bit, two digits are called a crumb, four digits are called a nibble, and eight digits are called a byte. An integer n may be represented in binary in Mathematica...
12.
Binary Plot -- from MathWorld - Weisstein, Eric W.
A binary plot of an integer sequence is a plot of the binary representations of successive terms where each term is represented as a column of bits with 1s colored black and 0s colored white. The columns are then placed side-by-side to yield an array of colored squares. Several examples are shown above for the positive integers n, square numbers n^2, Fibonacci numbers F_n, and binomial coefficients {n\choose k}. Binary plots can be extended to rational number sequences by placing the binary...
14.
Borrow -- from MathWorld - Weisstein, Eric W.
The procedure used in subtraction to "borrow" 10 from the next higher digit column in order to obtain a positive difference in the column in question. See also: Carry
15.
Calcus -- from MathWorld - Weisstein, Eric W.
\hbox{1 calcus} \equiv {{1\over 2304}}. See also: Half, Quarter, Scruple, Uncia, Unit Fraction
16.
Carry -- from MathWorld - Weisstein, Eric W.
The operating of shifting the leading digits of an addition into the next column to the left when the sum of that column exceeds a single digit (i.e., 9 in base 10). See also: Addend, Addition, Borrow
17.
Casting Out Nines -- from MathWorld - Weisstein, Eric W.
An elementary check of a multiplication which makes use of the congruence 10^n\equiv 1 (mod 9). Let decimal numbers be written a=a_n \dots a_2 a_1 a_0, b=b_n \dots b_2 b_1 b_0, and their product be c=c_n \dots c_2 c_1 c_0. Let the sums of the digits of these numbers be a^*, b^*, and c^*. Then a\equiv a^*\ \left({{\rm mod\ } {9}}\right), b\equiv b^*\ \left({{\rm mod\ } {9}}\right), and c\equiv c^*\ \left({{\rm mod\ } {9}}\right). Furthermore ab\equiv a^*b^*\ \left({{\rm mod\ } {9}}\right),...
18.
Casting Out Sevens -- from MathWorld - Weisstein, Eric W.
A method for verifying the correctness of an arithmetical operation on natural numbers, based on the same principle as casting out nines. The methods of sevens takes advantage of the fact that the residue (mod 7) of a sum (or product) must be equal to the sum (or product) of the residues of the summands (or factors). For example, the correct sum 45+34 =79 corresponds to a correct sum of residues mod 7 3+6=2, where, on the right-hand side, 9 has been replaced by its residue 2 (mod 7). ...
19.
Common Fraction -- from MathWorld - Weisstein, Eric W.
A common fraction is a fraction in which numerator and denominator are both integers, as opposed to fractions. For example, 2/5 is a common fraction, while {{{1\over 3}}\over{{2\over 5}}} is not. Common fractions are sometimes also called vulgar fractions. See also: Complex Fraction, Fraction, Improper Fraction, Mixed Fraction, Reduced Fraction
20.
Complex Addition -- from MathWorld - Weisstein, Eric W.
Two complex numbers z = x+iy and z'=x'+iy' are added together componentwise, z+z'=(x+x')+i(y+y'). In component form, (x,y)+(x',y')=(x+x',y+y') (Krantz 1999, p. 1). See also: Complex Division, Complex Multiplication, Complex Number, Complex Subtraction, Vector Addition
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