Well-defined expressionIn mathematics, a well-defined expression or unambiguous expression is an expression whose definition assigns it a unique interpretation or value. Otherwise, the expression is said to be not well defined, ill defined or ambiguous. A function is well defined if it gives the same result when the representation of the input is changed without changing the value of the input. For instance, if takes real numbers as input, and if does not equal then is not well defined (and thus not a function).
Euclidean algorithmIn mathematics, the Euclidean algorithm, or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers (numbers), the largest number that divides them both without a remainder. It is named after the ancient Greek mathematician Euclid, who first described it in his Elements (300 BC). It is an example of an algorithm, a step-by-step procedure for performing a calculation according to well-defined rules, and is one of the oldest algorithms in common use.
MonomialIn mathematics, a monomial is, roughly speaking, a polynomial which has only one term. Two definitions of a monomial may be encountered: A monomial, also called power product, is a product of powers of variables with nonnegative integer exponents, or, in other words, a product of variables, possibly with repetitions. For example, is a monomial. The constant is a monomial, being equal to the empty product and to for any variable . If only a single variable is considered, this means that a monomial is either or a power of , with a positive integer.
Dyadic rationalIn mathematics, a dyadic rational or binary rational is a number that can be expressed as a fraction whose denominator is a power of two. For example, 1/2, 3/2, and 3/8 are dyadic rationals, but 1/3 is not. These numbers are important in computer science because they are the only ones with finite binary representations. Dyadic rationals also have applications in weights and measures, musical time signatures, and early mathematics education. They can accurately approximate any real number.
ExponentiationIn mathematics, exponentiation is an operation involving two numbers, the base and the exponent or power. Exponentiation is written as bn, where b is the base and n is the power; this is pronounced as "b (raised) to the (power of) n". When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, bn is the product of multiplying n bases: The exponent is usually shown as a superscript to the right of the base.
Decimal separatorA decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form (e.g. "." in 12.45). Different countries officially designate different symbols for use as the separator. The choice of symbol also affects the choice of symbol for the thousands separator used in digit grouping. Any such symbol can be called a decimal mark, decimal marker, or decimal sign.
DecimalThe decimal numeral system (also called the base-ten positional numeral system and denary ˈdiːnəri or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (decimal fractions) of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as decimal notation. A decimal numeral (also often just decimal or, less correctly, decimal number), refers generally to the notation of a number in the decimal numeral system.
Continued fractionIn mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on. In a finite continued fraction (or terminated continued fraction), the iteration/recursion is terminated after finitely many steps by using an integer in lieu of another continued fraction. In contrast, an infinite continued fraction is an infinite expression.
MultiplicationMultiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product. The multiplication of whole numbers may be thought of as repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the multiplicand, as the quantity of the other one, the multiplier; both numbers can be referred to as factors.
Parts-per notationIn science and engineering, the parts-per notation is a set of pseudo-units to describe small values of miscellaneous dimensionless quantities, e.g. mole fraction or mass fraction. Since these fractions are quantity-per-quantity measures, they are pure numbers with no associated units of measurement. Commonly used are parts-per-million (ppm, 10−6), parts-per-billion (ppb, 10−9), parts-per-trillion (ppt, 10−12) and parts-per-quadrillion (ppq, 10−15). This notation is not part of the International System of Units (SI) system and its meaning is ambiguous.
Slash (punctuation)The slash is the oblique slanting line punctuation mark . Also known as a stroke, a solidus, a forward slash or several other historical or technical names including oblique and virgule. Once used to mark periods and commas, the slash is now used to represent division and fractions, exclusive 'or' and inclusive 'or', and as a date separator. A slash in the reverse direction is known as a backslash. Slashes may be found in early writing as a variant form of dashes, vertical strokes, etc.
Elementary arithmeticElementary arithmetic is a branch of mathematics involving basic numerical operations, namely addition, subtraction, multiplication, and division. Due to its low level of abstraction, broad range of application, and being the foundation of all mathematics, elementary arithmetic is generally the first critical branch of mathematics to be taught in schools. Numerical digit Symbols called digits are used to represent the value of numbers in a numeral system. The most commonly used digits are the Arabic numerals (0 to 9).
