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A tree with a finite number of branches at each fork and with a finite number of leaves at the end of each branch is called a finitely branching tree. König's lemma states ...

The l^2-norm (also written "l^2-norm") |x| is a vector norm defined for a complex vector x=[x_1; x_2; |; x_n] (1) by |x|=sqrt(sum_(k=1)^n|x_k|^2), (2) where |x_k| on the ...

In practice, the vertical offsets from a line (polynomial, surface, hyperplane, etc.) are almost always minimized instead of the perpendicular offsets. This provides a ...

A Lehner continued fraction is a generalized continued fraction of the form b_0+(e_1)/(b_1+(e_2)/(b_2+(e_3)/(b_3+...))) where (b_i,e_(i+1))=(1,1) or (2, -1) for x in [1,2) an ...

The case of the Weierstrass elliptic function with invariants g_2=1 and g_3=0. In this case, the half-periods are given by (omega_1,omega_2)=(omega,iomega), where omega is ...

A Liouville number is a transcendental number which has very close rational number approximations. An irrational number beta is called a Liouville number if, for each n, ...

The symbol o(x), pronounced "little-O of x," is one of the Landau symbols and is used to symbolically express the asymptotic behavior of a given function. In particular, if n ...

A mathematical property P holds locally if P is true near every point. In many different areas of mathematics, this notion is very useful. For instance, the sphere, and more ...

A topology tau on a topological vector space X=(X,tau) (with X usually assumed to be T2) is said to be locally convex if tau admits a local base at 0 consisting of balanced, ...

The mean triangle area A^_ is the average area of a triangle in triangle picking within some given shape. As summarized in the following table, it is possible to compute the ...