Question

10. a) Give one example for the following. Justify your choice of examples.
i) A bounded set having no limit point.
ii) A bounded set having infinite number of limit points.
iii) A infinite compact set which is not an interval. (6)
b) Prove that the function f defined by




−
=
,4 if is irrational
,4 if is rational
( )
x
x
f x
is discontinuous at each real number, using the sequential definition of continuity. (4)