So I start with :
which breaks down to :
But I'm confused how to bound this to get a delta.
(PS: I cant figure out how to put the absolute value signs in here, but I know they are supposed to be there)
Do I break it down to :
if 0 < a < b < c, then 0 < a2 < ab < b2 < bc < c2, or in short:
0 < a2 < b2 < c2.
similarly, if 0 < a < b < c then:
0 < 1/c < 1/b < 1/a
the basis for the last inequality is this:
we define for two fractions a/b, c/d: a/b < c/d if and only if ad < bc. note this agrees with our usual notion if b = d = 1.
this means that if a < c, that when we compare:
1/a and 1/c, we have 1(c) > a(1), so 1/a > 1/c.
for example: 4 is bigger than 2, so 1/4 is smaller than 1/2.