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The p-adic norm satisfies |x+y|_p<=max(|x|_p,|y|_p) for all x and y.

int_a^bf_1(x)dxint_a^bf_2(x)dx...int_a^bf_n(x)dx <=(b-a)^(n-1)int_a^bf_1(x)f_2(x)...f_n(x)dx, where f_1, f_2, ..., f_n are nonnegative integrable functions on [a,b] which are ...

phi(A)+phi(B)-phi(A union B)>=phi(A intersection B).

For a braid with M strands, R components, P positive crossings, and N negative crossings, {P-N<=U_++M-R if P>=N; P-N<=U_-+M-R if P<=N, (1) where U_+/- are the smallest number ...

Let S_n be the sum of n random variates X_i with a Bernoulli distribution with P(X_i=1)=p_i. Then sum_(k=0)^infty|P(S_n=k)-(e^(-lambda)lambda^k)/(k!)|<2sum_(i=1)^np_i^2, ...

Let chi be a nonprincipal number theoretic character over Z/Zn. Then for any integer h, |sum_(x=1)^hchi(x)|<=2sqrt(n)lnn.

Given T an unbiased estimator of theta so that <T>=theta. Then var(T)>=1/(Nint_(-infty)^infty[(partial(lnf))/(partialtheta)]^2fdx), where var is the variance.

Relates invariants of a curve defined over the integers. If this inequality were proven true, then Fermat's last theorem would follow for sufficiently large exponents. ...

A balanced incomplete block design (v, k, lambda, r, b) exists only for b>=v (or, equivalently, r>=k).

Let y_n be a complex number for 1<=n<=N and let y_n=0 if n<1 or n>N. Then (Montgomery 2001).