Seems like to find a counterexample you find some continous function f. Define f' to be f when f =/= sup and 0 when it is. Because it's a continuous function you can find points in the image of f arbitrarily close to sup f so sup f' = sup f, but sup f is not in f' because we removed it.
Generalization is dual to localization. Minimum is dual to maximum, infimum is dual to supremum. Convergent (syntropy) is dual to divergent (entropy) -- the 4th law of thermodynamics! Points are dual to lines -- the principle of duality in geometry. "Always two there are" -- Yoda.
This is pure gold. Thanks for the opportunity to learn from you.
Simple and elegant proof. Very nice!
Most wonderful video ❤️❤️
Many many thanks
Thanks a lot!! :)
Ich finde das Bild im Thumbnail EXTRAM gut, das erklärt eig schon alles =D
Thanks :)
Seems like to find a counterexample you find some continous function f. Define f' to be f when f =/= sup and 0 when it is. Because it's a continuous function you can find points in the image of f arbitrarily close to sup f so sup f' = sup f, but sup f is not in f' because we removed it.
is it called extreme value thm?
Generalization is dual to localization.
Minimum is dual to maximum, infimum is dual to supremum.
Convergent (syntropy) is dual to divergent (entropy) -- the 4th law of thermodynamics!
Points are dual to lines -- the principle of duality in geometry.
"Always two there are" -- Yoda.