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A set of elements S is said to be infinite if the elements of a proper subset S^' can be put into one-to-one correspondence with the elements of S. An infinite set whose ...

A proof which indirectly shows a mathematical object exists without providing a specific example or algorithm for producing an example. Nonconstructive proofs are also called ...

The truth of an infinite sequence of propositions P_i for i=1, ..., infty is established if (1) P_1 is true, and (2) P_k implies P_(k+1) for all k. This principle is ...

The term "real line" has a number of different meanings in mathematics. Most commonly, "real line" is used to mean real axis, i.e., a line with a fixed scale so that every ...

A single axiom that is satisfied only by NAND or NOR must be of the form "something equals a," since otherwise constant functions would satisfy the equation. With up to six ...

e^(i(ntheta))=(e^(itheta))^n. (1) From the Euler formula it follows that cos(ntheta)+isin(ntheta)=(costheta+isintheta)^n. (2) A similar identity holds for the hyperbolic ...

A technique used by André (1887) to provide an elegant solution to the ballot problem (Hilton and Pederson 1991) and in study of Wiener processes (Doob 1953; Papoulis 1984, ...

The map x_(n+1)=2mux_n, (1) where x is computed modulo 1. A generalized Baker's map can be defined as x_(n+1) = {lambda_ax_n y_n<alpha ; (1-lambda_b)+lambda_bx_n y_n>alpha ...

Let A and B_j be sets. Conditional probability requires that P(A intersection B_j)=P(A)P(B_j|A), (1) where intersection denotes intersection ("and"), and also that P(A ...

The Benney equation in 1+1 dimensions is the nonlinear partial differential equation ...