Find a real-valued function, f, with domain [0,1] such that
a) f(0) < f(1)
b) f is continuous
c) For all a and b, where 0 < a < b < 1, f is not increasing on [a,b]
Tip: First think about different functions that aren't increasing an interval.
Also, try to define f in a concise way (using formulas).
My sister went with this professor and he gave this problem to her and us. Cant figure it...
Have you came across the Cantor function c(x) on the unit interval? What do you get if you subtract a small multiple of x from it, for example the function ?
Have you came across the Cantor function c(x) on the unit interval? What do you get if you subtract a small multiple of x from it, for example the function ?
Wow thats pretty awesome.
But how exactly do I define f(x) in a 'precise' way? What exactly is c(x)?