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An existential sentence is a statement claiming the existence of an object with given properties. In the language of set theory it can be formulated as follows, exists x in U ...

Draw a triangle DeltaA_1A_2A_3, and let A_1^' be the intersection of the parallel to A_3A_1 through A_2 (the A_2-exmedian) and the parallel to A_1A_2 through A_3 (the ...

The exponential factorial is defined by the recurrence relation a_n=n^(a_(n-1)), (1) where a_0=1. The first few terms are therefore a_1 = 1 (2) a_2 = 2^1=2 (3) a_3 = ...

On a Lie group, exp is a map from the Lie algebra to its Lie group. If you think of the Lie algebra as the tangent space to the identity of the Lie group, exp(v) is defined ...

The extangents circle is the circumcircle of the extangents triangle. Its center function is a complicated 9th-order polynomial and its circle function is a complicated ...

A extension ring (or ring extension) of a ring R is any ring S of which R is a subring. For example, the field of rational numbers Q and the ring of Gaussian integers Z[i] ...

The exterior derivative of a function f is the one-form df=sum_(i)(partialf)/(partialx_i)dx_i (1) written in a coordinate chart (x_1,...,x_n). Thinking of a function as a ...

The extouch triangle DeltaT_1T_2T_3 is the triangle formed by the points of tangency of a triangle DeltaA_1A_2A_3 with its excircles J_1, J_2, and J_3. The points T_1, T_2, ...

Given a subset K of a vector space X, a nonempty subset S subset K is called an extreme set of K if no point of S is an internal point of any line interval whose endpoints ...

A subset F subset R of the real numbers is said to be an F_sigma set provided F is the countable union of closed sets. The name F_sigma comes from French: The F stands for ...