(a) Show that the function given
by ()=(-1)(-2)
is not continuous, where denotes
"integer part", as usual. In other words, show that
there is a sequence ()
such that for some , we have
and ()
but with ().
(b) Find all the integer points such that
is continuous at . Prove your assertion(s).
(c) Find all the integer points such that
()=(-1)2 is continuous at .
Prove your assertion(s).