Use the triangle inequality to show that if a and be are in R, with a not equal to b, then there exists an open interval U centered at a and V centered at b, both of radius epsilon= 1/2 abs[a-b] , with U/\V= 0 (intersection)
I really don't know what I wanna do here. I'm imagining a line centered at A and another at b with radius epsilon something like this =>
----- (-e)-------a-------(e)------
-----(-e)--------b-------(e)-----
ok I follow this, but if I need to use the triangle property how do i go about using it?
A friend told me:
let u= (a-e, a+e) = absolute value(c-a) < e for c in R
let v= (b-e, b+e) = absolute value(d-a) < e for d in R
then absloutevalue(x-a) < e = 1/2absloute(a-b)
absloute value(x-b) < e = 1/2absloute(a-b)
is this correct? and if so....how does he go from abs(c-a) < e to
abs(x-a) < e
and then to = 1/2 abs(a-b)