Answer:
<em>Why might he think that and what would you tell him?</em>
He thought perhaps that numbers were formed by rational numbers of the form , where
. I would tell him that there are rational numbers
, such that
, where
,
,
.
<em>Is there a number that falls between these?</em>
is a rational number between
and
.
Step-by-step explanation:
<em>Why might he think that and what would you tell him?</em>
He thought perhaps that numbers were formed by rational numbers of the form , where
. I would tell him that there are rational numbers
, such that
, where
,
,
.
<em>Is there a number that falls between these?</em>
Indeed, the average number of and
, for instance. That is:
is a rational number between
and
.