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Inequalities: In mathematics, an inequality is a statement that compares two values or expressions, showing that one is greater than, less than, or equal to the other. Inequalities are commonly represented using symbols such as "" (greater than), "=" (greater than or equal to), and " =" (not equal to). Inequalities play an important role in many areas of mathematics, including algebra, analysis, and optimization.Uniform Norms: A uniform norm is a way of measuring the size or magnitude of a function or sequence of functions. Specifically, the uniform norm of a function is defined as the maximum value that the function attains over a given domain. In other words, the uniform norm of a function f(x) over the interval a, b] is given by f_∞ = sup{f(x): x in a, b]}, where sup denotes the supremum or least upper bound of a set. Uniform norms are widely used in functional analysis and other areas of mathematics to measure the distance between functions or to define convergence.Zeros: In mathematics, a zero (or root) of a function is a value of the independent variable for which the function evaluates to zero. In other words, a zero of a function f(x) is a value x such that f(x) = 0. Zeros are important because they represent the points where the graph of the function intersects the x-axis. Zeros can be found using various methods, including factoring, the quadratic formula, and numerical methods such as Newton's method.Polynomials: A polynomial is a mathematical expression consisting of variables (usually denoted by x, y, or z) and coefficients (usually real or complex numbers) that are combined using addition, subtraction, and multiplication, but not division by a variable. The degree of a polynomial is the highest power of the variable in the expression, and the leading coefficient is the coefficient of the term with the highest power. Polynomials play a fundamental role in many areas of mathematics, including algebra, analysis, geometry, and number theory. They are used to model various phenomena in science, engineering, and economics, and to solve problems in optimization, approximation, and data analysis.