Differences
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sav08:fixpoints [2008/04/30 10:48] vkuncak created |
sav08:fixpoints [2008/05/06 23:31] giuliano |
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| Note: | Note: | ||
| * 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 | + | * $f(x)=x$ the set of fixedpoints is $\mathbb Z$ |
| - | * $f(x)=x^2$ the set of fixedpoints is | + | * $f(x)=x^2$ the set of fixedpoints is $\{0, 1\}$ |
| - | * $f(x)=3x-6$ has exactly one fixpoint | + | * $f(x)=3x-6$ 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 | ||