# Differences

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 sav08:fixpoints [2008/05/06 23:30]giuliano sav08:fixpoints [2008/05/06 23:31] (current)giuliano Both sides previous revision Previous revision 2008/05/06 23:31 giuliano 2008/05/06 23:30 giuliano 2008/04/30 10:48 vkuncak created 2008/05/06 23:31 giuliano 2008/05/06 23:30 giuliano 2008/04/30 10:48 vkuncak created Line 8: Line 8: * a function can have various number of fixpoints. Take $f : {\cal Z} \to {\cal Z}$, * a function can have various number of fixpoints. Take $f : {\cal Z} \to {\cal Z}$, * $f(x)=x$ the set of fixedpoints is $\mathbb Z$ * $f(x)=x$ the set of fixedpoints is $\mathbb Z$ - * $f(x)=x^2$ the set of fixedpoints is ${0, 1}$ + * $f(x)=x^2$ the set of fixedpoints is $\{0, 1\}$ * $f(x)=3x-6$ has exactly one fixpoint: $3$ * $f(x)=3x-6$ has exactly one fixpoint: $3$ * a function can have at most one least and at most one greatest fixpoint * a function can have at most one least and at most one greatest fixpoint