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A three-dimensional shadow of a four-dimensional Klein bottle.

The identity element I (also denoted E, e, or 1) of a group or related mathematical structure S is the unique element such that Ia=aI=a for every element a in S. The symbol ...

If f:D->Y is a map (a.k.a. function, transformation, etc.) over a domain D, then the image of f, also called the range of D under f, is defined as the set of all values that ...

An infinitesimal is some quantity that is explicitly nonzero and yet smaller in absolute value than any real quantity. The understanding of infinitesimals was a major ...

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 ...

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 ...

A definition of a set by mentioning a defining property.

The term used in propositional calculus for the NOR connective. The notation AvB is used for this connective.

The throwing and catching of multiple objects such that at least one is always in the air. Some aspects of juggling turn out to be quite mathematical. The best examples are ...

A point of discontinuity, also called a leap.