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Arrow's paradox, also called Arrow's impossibility theorem or the general possibility theorem, states that perfect democratic voting is impossible, not just in practice but ...

The conditional probability of an event A assuming that B has occurred, denoted P(A|B), equals P(A|B)=(P(A intersection B))/(P(B)), (1) which can be proven directly using a ...

The property of being continuous.

The mathematical study of how to manipulate the parameters affecting the behavior of a system to produce the desired or optimal outcome.

A ring without zero divisors in which an integer norm and an associated division algorithm (i.e., a Euclidean algorithm) can be defined. For signed integers, the usual norm ...

Let D=D(z_0,R) be an open disk, and let u be a harmonic function on D such that u(z)>=0 for all z in D. Then for all z in D, we have 0<=u(z)<=(R/(R-|z-z_0|))^2u(z_0).

The parameter r in the exponential equation of population growth N(t)=N_0e^(rt), where N_0 is the initial population size (at t=0) and t is the elapsed time.

All elementary functions can be extended to the complex plane. Such definitions agree with the real definitions on the x-axis and constitute an analytic continuation.

Rényi entropy is defined as: H_alpha(p_1,p_2,...,p_n)=1/(1-alpha)ln(sum_(i=1)^np_i^alpha), where alpha>0, alpha!=1. As alpha->1, H_alpha(p_1,p_2,...,p_n) converges to ...

An analytic function f on the unit disk is called schlicht if 1. f is one-to-one, 2. f(0)=0, and 3. f^'(0)=1, in which case it is written f in S. Schlicht functions have ...