Square (algebra)In mathematics, a square is the result of multiplying a number by itself. The verb "to square" is used to denote this operation. Squaring is the same as raising to the power 2, and is denoted by a superscript 2; for instance, the square of 3 may be written as 32, which is the number 9. In some cases when superscripts are not available, as for instance in programming languages or plain text files, the notations x^2 (caret) or x**2 may be used in place of x2.
Distributive propertyIn mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality x⋅(y+z)=x⋅y+x⋅z{\displaystyle x\cdot (y+z)=x\cdot y+x\cdot z} is always true in elementary algebra. For example, in elementary arithmetic, one has 2⋅(1+3)=(2⋅1)+(2⋅3).{\displaystyle 2\cdot (1+3)=(2\cdot 1)+(2\cdot 3).} Therefore, one would say that multiplicationdistributes over addition.
Commutative propertyIn mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Perhaps most familiar as a property of arithmetic, e.g. "3 + 4 = 4 + 3" or "2 × 5 = 5 × 2", the property can also be used in more advanced settings.
Negative numberIn mathematics, a negative number is the opposite of a positive real number. Equivalently, a negative number is a real number that is less thanzero. Negative numbers are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset.
Field (mathematics)In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational numbers do. Fields are fundamental algebraic structures that are widely used in algebra, number theory, and many other areas of mathematics. The best known fields are the field of rational numbers, the field of real numbers, and the field of complex numbers.
Associative propertyIn mathematics, the associative property is a property of some binary operations that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs.
Square rootNumber whose square is a given numberNotation for the (principal) square root of x.For example, √25 = 5, since 25 = 5 ⋅ 5, or 5 (5 squared).In mathematics, a square root of a number x is a number y such that y2=x{\displaystyle y^{2}=x}; in other words, a number y whose square (the result of multiplying the number by itself, or y⋅y{\displaystyle y\cdot y}) is x. For example, 4 and −4 are square roots of 16 because 42=(−4)2=16{\displaystyle 4^{2}=(-4)^{2}=16}.
Imaginary unitThe imaginary unit, usually denoted by i, is a mathematical constant that is a solution to the quadratic equation x2 = −1, which is not solved by any real number. Any real-number multiple of the imaginary unit is called an imaginary number.
Real numberNumber representing a continuous quantityReal numbers can be thought of as all points on a number line.In mathematics, a real number is a number that can be used to measure a continuous one-dimensionalquantity such as a length, duration or temperature. Here, continuous means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion.
MathematicsField of knowledgeIlluminated letter P at the beginning of Adelard of Bath's translation of Euclid's Elements, which starts "Punctum est illud cui pars non est" ('A point is that which has no part'). Geometry is shown personified as a woman, following Martianus Capella's De nuptiis Philologiae et Mercurii.Mathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities.ArithmeticArithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. Arithmetic systems can be distinguished based on the type of numbers they operate on. Integer arithmetic is about calculations with positive and negative integers. Rational number arithmetic involves operations on fractions of integers.
NumberA number is a mathematical object used to count, measure, order and label. The most basic examples are the natural numbers: 1, 2, 3, 4, 5, and so forth. Individual numbers can be represented in spoken or written language with number words, or with dedicated symbols called numerals; for example, "eleven" is a number word and "11" is the corresponding numeral.*As an Amazon Associate I earn from qualifying purchases.