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A sequence {x_n} is called an infinitive sequence if, for every i, x_n=i for infinitely many n. Write a(i,j) for the jth index n for which x_n=i. Then as i and j range ...

Conditions at an initial time t=t_0 from which a given set of mathematical equations or physical system evolves. A system with initial conditions specified is known as an ...

In a category C, an initial object is an object I in Ob(C) such that for any other object X in Ob(C), there is one and only one morphism from I to X.

An injective patch is a patch such that x(u_1,v_1)=x(u_2,v_2) implies that u_1=u_2 and v_1=v_2. An example of a patch which is injective but not regular is the function ...

An inner automorphism of a group G is an automorphism of the form phi(g)=h^(-1)gh, where h is a fixed element of G. The automorphism of the symmetric group S_3 that maps the ...

A particular type of automorphism group which exists only for groups. For a group G, the inner automorphism group is defined by Inn(G)={sigma_a:a in G} subset Aut(G) where ...

Externally erect a square on the side BC. Now join the new vertices S_(AB) and S_AC of this square with the vertex A, marking the points of intersection Q_(A,BC) and ...

An inner product space is a vector space together with an inner product on it. If the inner product defines a complete metric, then the inner product space is called a ...

The inner Vecten circle is the circumcircle of the inner Vecten triangle. It has center at Kimberling center X_(642), which is the complement of the inner Vecten point ...

An inscribed angle is an angle ∠ABC formed by points A, B, and C on a circle's circumference as illustrated above. For an inscribed angle ∠ABC and central angle ∠AOC with the ...