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Definitions about a set which depend on the entire set.

A divisor which is not a proper divisor.

A fixed point for which the stability matrix has equal nonzero eigenvectors.

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.

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 ...

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.