• English only

# Differences

This shows you the differences between two versions of the page.

sav08:fixpoints [2008/05/06 23:30]
giuliano
sav08:fixpoints [2008/05/06 23:31] (current)
giuliano
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