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Functii crescatoare

 
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elena_romina
Euclid


Joined: 15 Nov 2008
Posts: 40
PostPosted: Fri Sep 18, 2009 7:03 am    Post subject: Functii crescatoare Reply with quote
De ce nu putem vedea daca o functie e crescatoare calculand f(x+1)-f(x) si apoi comparand cu 0, la fel ca la siruri?
multumesc
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Marius Mainea
Gauss


Joined: 26 May 2008
Posts: 1075
Location: Gaesti (Dambovita)
PostPosted: Fri Sep 18, 2009 7:29 am    Post subject: Reply with quote
Deoarece functia lui Dirichlet

f(x)=\left{\begin{array}{cc}1&\mbox{daca}&x\in\mathbb{Q}\\0&\mbox{daca}& x\notin\mathbb{Q}\end{array}

nu este crescatoare desi f(x+1)-f(x)\ge 0 pentru orice x real.
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