MAT237Y1 : mat237 1-3inequality.pdf

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Inequality 1. 3 is a very important inequality which can be used as a legitimate tool (fact) about norm of a n-tuple in relation to the absolute value of the components of the n-tuple. If we were to say the magnitude of a vector xxx = (x1, x2, . xn) is small, according to inequality 1. 3 we could instead say that the maximum the magnitudes of the components is small. For a number n to have |xxx| < n is guaranteed if. Similarly for m < |xxx| it is su cient that m < max{|x1|,|x2|, . This inequality can simplify our calculations about limit of function of several variables, and later this can be important in working with vector valued functions. See for example the discussion in the middle of page 14, or the bottom of page 108. In general whenever the passage from vector to scalar is needed the inequality.