Version 6.0 added a collection of carefully optimized functions to Mathematica's powerful arsenal of numerical handling capabilities.

x >= y or x >= y yields True if x is determined to be greater than or equal to y. x_1 >= x_2 >= x_3 yields True if the x_i form a non-increasing sequence.

x > y yields True if x is determined to be greater than y. x_1 > x_2 > x_3 yields True if the x_i form a strictly decreasing sequence.

x <= y or x <= y yields True if x is determined to be less than or equal to y. x_1 <= x_2 <= x_3 yields True if the x TraditionalForm\`i form a nondecreasing sequence.

x < y yields True if x is determined to be less than y. x_1 < x_2 < x_3 yields True if the x_i form a strictly increasing sequence.

ContinuousWaveletData[{{oct_1, voc_1} -> coef_1, ...}, wave] yields a continuous wavelet data object with wavelet coefficients coef_i corresponding to octave and voice ...

NegativeBinomialDistribution[n, p] represents a negative binomial distribution with parameters n and p.

RemoteService[properties] contains a list of properties about a service provided by a Lightweight Grid Manager.

Overtones is an option to Waveform that specifies the number of overtones to be present in a standard waveform when created with Fourier summation.

ChromaticPolynomial[g, z] gives the chromatic polynomial P(z) of graph g, which counts the number of ways to color g with, at most, z colors.