# Differences

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

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