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Three elements x, y and z of a set S are said to be associative under a binary operation * if they satisfy x*(y*z)=(x*y)*z. (1) Real numbers are associative under addition ...

An asymptote is a line or curve that approaches a given curve arbitrarily closely, as illustrated in the above diagram. The plot above shows 1/x, which has a vertical ...

While some authors define "circumference" as distance around an arbitrary closed object (sometimes restricted to a closed curved object), in the work, the term "perimeter" is ...

A multiplicative factor (usually indexed) such as one of the constants a_i in the polynomial a_nx^n+a_(n-1)x^(n-1)+...+a_2x^2+a_1x+a_0. In this polynomial, the monomials are ...

Cohomology is an invariant of a topological space, formally "dual" to homology, and so it detects "holes" in a space. Cohomology has more algebraic structure than homology, ...

Cohomotopy groups are similar to homotopy groups. A cohomotopy group is a group related to the homotopy classes of maps from a space X into a sphere S^n.

Two elements x and y of a set S are said to be commutative under a binary operation * if they satisfy x*y=y*x. (1) Real numbers are commutative under addition x+y=y+x (2) and ...

Two angles alpha and beta are said to be complementary if alpha+beta=pi/2. In other words, alpha and beta are complementary angles if they produce a right angle when combined.

A conclusion is a statement arrived at by applying a set of logical rules known as syllogisms to a set of premises. The process of drawing conclusions from premises and ...

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 ...