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An operator A^~ such that A^~^2=A^~ or an element of an algebra x such that x^2=x.

Definitions about a set which depend on the entire set.

A curve created by starting with a circle, dividing it into six arcs, and flipping three alternating arcs. The process is then repeated an infinite number of times.

An archaic term for calculus.

The Jordan product of quantities x and y is defined by x·y=1/2(xy+yx).

An algorithm which constructs allowed mathematical statements from simple ingredients.

The appropriate notion of integer for surreal numbers.

A geometry constructed without reference to measurement. The only primitive concepts are those of points and intermediacy. There are 10 axioms underlying ordered geometry.

Two (or more) intersecting curves that are perpendicular at their intersection are said to be orthogonal.

A partial function is a function that is not total.