Carmichael's theorem describes prime divisors in ones named for Edouard Lucas, which are described by a rational generating function.
One of these things describes homology groups of a space in terms of the homology groups of two subspaces and their intersection and is named for Mayer and Vietoris. A commutative diagram of R-modules with two exact rows yields one of these things by the snake lemma. Carmichael's theorem describes prime divisors in ones named for Edouard Lucas, which are described by a rational generating function. The Bolzano-Weierstrass theorem states that every bounded one in R-n has a subset that converges to a finite limit. A complete metric space is defined by the convergence of ones named for Cauchy. Although not functions, the squeeze theorem can be used to find their limit. These things can be defined by a recurrence relation, such as the one F-sub-n equals F-sub-n-minus-one plus F-sub-n-minus-two. For 10 points, name these ordered lists of numbers that include one named for Fibonacci.
One of these things describes homology groups of a space in terms of the homology groups of two subspaces and their intersection and is named for Mayer and Vietoris.
sequence [accept sequential; accept \"long exact sequence\" before John Farey, Sr.]