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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.

A word or string which is not admissible.

Two objects which touch each other are said to be incident.

For a sequence {a_n}, if a_(n+1)-a_n>0 for n>=x, then a_n is increasing for n>=x. Conversely, if a_(n+1)-a_n<0 for n>=x, then a_n is decreasing for n>=x. If a_n>0 and ...

The number of inward directed graph edges from a given graph vertex in a directed graph.

A spherical image of a curve. The most common indicatrix is Dupin's indicatrix.

If f:(X,A)->(Y,B) is homotopic to g:(X,A)->(Y,B), then f_*:H_n(X,A)->H_n(Y,B) and g_*:H_n(X,A)->H_n(Y,B) are said to be the induced maps.

The fifth of Peano's axioms, which states: If a set S of numbers contains zero and also the successor of every number in S, then every number is in S.

While an equality A=B states that two mathematical expressions are equal, an inequation A!=B states that two expressions are not equal.

A group having an infinite number of elements. Some infinite groups, such as the integers or rationals, are not continuous groups.