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Consider expressions built up from variables and constants using function symbols. If v_1, ..., v_n are variables and t_1, ..., t_n are expressions, then a set of mappings ...

The union of two sets A and B is the set obtained by combining the members of each. This is written A union B, and is pronounced "A union B" or "A cup B." The union of sets ...

Transfinite induction, like regular induction, is used to show a property P(n) holds for all numbers n. The essential difference is that regular induction is restricted to ...

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.