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In mathematics, a "norm" is a function that assigns a non-negative real number to a vector in a vector space, analogous to its length. This "normed" entity is a mathematical object upon which a norm is defined. The Cauchy-Schwarz inequality, for instance, uses norms to analyze relationships between functions, vectors, or integrals. Norms are fundamental in areas like functional analysis, statistics, and probability theory.123

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