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The Bernoulli inequality states (1+x)^n>1+nx, (1) where x>-1!=0 is a real number and n>1 an integer. This inequality can be proven by taking a Maclaurin series of (1+x)^n, ...

For c<1, x^c<1+c(x-1). For c>1, x^c>1+c(x-1).

Let Omega be an open, bounded, and connected subset of R^d for some d and let dx denote d-dimensional Lebesgue measure on R^d. In functional analysis, the Friedrichs ...

Let x and y be vectors. Then the triangle inequality is given by |x|-|y|<=|x+y|<=|x|+|y|. (1) Equivalently, for complex numbers z_1 and z_2, ...

The signature of a non-degenerate quadratic form Q=y_1^2+y_2^2+...+y_p^2-y_(p+1)^2-y_(p+2)^2-...-y_r^2 of rank r is most often defined to be the ordered pair (p,q)=(p,r-p) of ...

The inequality (j+1)a_j+a_i>=(j+1)i, which is satisfied by all A-sequences.

For 0<=x<=pi/2, 2/pix<=sinx<=x.

For b>a>0, 1/b<(lnb-lna)/(b-a)<1/a.

An inequality is strict if replacing any "less than" and "greater than" signs with equal signs never gives a true expression. For example, a<=b is not strict, whereas a<b is.

An imaginary quadratic field is a quadratic field Q(sqrt(D)) with D<0. Special cases are summarized in the following table. D field members -1 Gaussian integer -3 Eisenstein ...