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The square root inequality states that 2sqrt(n+1)-2sqrt(n)<1/(sqrt(n))<2sqrt(n)-2sqrt(n-1) for n>=1.

The robustness of a given outcome to small changes in initial conditions or small random fluctuations. Chaos is an example of a process which is not stable.

The value at a stationary point.

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

An equation or formula involving transcendental functions.

A specific type of ultraproduct that can be used to construct nonstandard universes and obtain the transfer principle as a corollary of Łoś' theorem for ultraproducts.

A function of a single variable (e.g., f(x), g(z), theta(xi), etc.).

A function f(x) is said to be antiperiodic with antiperiod p if -f(x)=f(x+np) for n=1, 3, .... For example, the sine function sinx is antiperiodic with period pi (as well as ...

The study of the nature and properties of bifurcations.

f(x)=C_psiint_(-infty)^inftyint_(-infty)^infty<f,psi^(a,b)>psi^(a,b)(x)a^(-2)dadb, where psi^(a,b)(x)=|a|^(-1/2)psi((x-b)/a). This result was originally derived using ...