Search results
Results from the WOW.Com Content Network
The most common symbols of grouping are the parentheses and the square brackets, and the latter are usually used to avoid too many repeated parentheses. For example, to indicate the product of binomials, parentheses are usually used, thus: ( 2 x + 3 ) ( 3 x + 4 ) {\displaystyle (2x+3)(3x+4)} .
In elementary algebra, parentheses ( ) are used to specify the order of operations. [1] Terms inside the bracket are evaluated first; hence 2×(3 + 4) is 14, 20 ÷ (5(1 + 1)) is 2 and (2×3) + 4 is 10. This notation is extended to cover more general algebra involving variables: for example (x + y) × (x − y). Square brackets are also often ...
[2] The Dyck language with two distinct types of brackets can be recognized in the complexity class. [3] The number of distinct Dyck words with exactly n pairs of parentheses and k innermost pairs (viz. the substring [ ]) is the Narayana number (,).
The proof that the language of balanced (i.e., properly nested) parentheses is not regular follows the same idea. Given p {\displaystyle p} , there is a string of balanced parentheses that begins with more than p {\displaystyle p} left parentheses, so that y {\displaystyle y} will consist entirely of left parentheses.
In the equation 7x − 5 = 2, the sides of the equation are expressions. In mathematics, an expression is a written arrangement of symbols following the context-dependent, syntactic conventions of mathematical notation. Symbols can denote numbers, variables, operations, and functions. [1]
In mathematics, specifically algebraic geometry, a period or algebraic period [1] is a complex number that can be expressed as an integral of an algebraic function over an algebraic domain. The periods are a class of numbers which includes, alongside the algebraic numbers, many well known mathematical constants such as the number π .
Consider the vectors (polynomials) p 1 := 1, p 2 := x + 1, and p 3 := x 2 + x + 1. Is the polynomial x 2 − 1 a linear combination of p 1, p 2, and p 3? To find out, consider an arbitrary linear combination of these vectors and try to see when it equals the desired vector x 2 − 1. Picking arbitrary coefficients a 1, a 2, and a 3, we want
The Legendre polynomials were first introduced in 1782 by Adrien-Marie Legendre [3] as the coefficients in the expansion of the Newtonian potential | ′ | = + ′ ′ = = ′ + (), where r and r′ are the lengths of the vectors x and x′ respectively and γ is the angle between those two vectors.