0
votes
1answer
77 views

continuous and bounded function without maximum or minimum

Give an example that contradicts this sentence : $f:(0,1]\to\Bbb R$ is a continuous and bounded function in $(0,1]$ then : $f$ has maximum or minimum. I have understood that $\sin(1/x)$ could be a ...
4
votes
1answer
160 views

Nonexistence of a strongly multiplicative increasing function with $f(2)=3$

Show that there does not exist a strictly increasing function $f:\mathbb{N}\rightarrow\mathbb{N}$ satisfying $$f(2)=3$$ $$f(mn)=f(m)f(n)\forall m,n\in\mathbb{N}$$ Progress: Assume the ...