Let be a continuous function defined for
. If
takes rational values for all
and
then the value of
is
7.5
10
5
infinite
As is continuous in
will attain all values between
and
. As
takes rational values for all
and there are innumerable irrational values between
and
,
can take rational values for all
if
has a constant rational value at all points between
and
. So,
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