I am attempting to show that there does not exist an N past which every open unit interval (k, k+1) -where k is an integer- contains a zero of the following function:
$[\sqrt(x)]$ is the lowest integer of the square root of
$x$. Any thoughts?
I had figured that I could consider the interval
$(i^2, (i+1)^2)$ in which h(x) is described by the function
Then try to see on what unit intervals (k, k+1) in here contain a zero of
$h_n$ then try to show that
$((i+1)^2, (i+2)^2)$ also has such an interval, but I am running out of ideas.