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In mathematics, the Khintchine inequality, named after Aleksandr Khinchin and spelled in multiple ways in the Latin alphabet, is a theorem from probability, and is also frequently used in analysis. Heuristically, it says that if we pick N {\displaystyle N} complex numbers x 1 , … , x N ∈ C {\displaystyle x_{1},\dots ,x_{N}\in \mathbb {C} } , and add them together each multiplied by a random sign ± 1 {\displaystyle \pm 1} , then the expected value of the sum's modulus, or the modulus it will be closest to on average, will be not too far off from | x 1 | 2 + ⋯ + | x N | 2 {\displaystyle {\sqrt {|x_{1}|^{2}+\cdots +|x_{N}|^{2}}}}.