- #1
Andrax
- 117
- 0
Homework Statement
so this is the question I've trid my best (over 2 hours trynig this and failed) can someone please help me
show that :
l a l < 1 and l b l<1 => l a + b l < l 1 + ab l
Homework Equations
just a little bit on info , you can only stay from the lal < 1 and lbl <1 side to get to the other one
The Attempt at a Solution
here's what i tried so fay
l a l < 1 and l b l<1 => l a b l < 1
=> -1 < ab < 1
=> 0 < 1 + ab <2
=> l 1 + ab l <2
l a l < 1 and l b l<1 => -2 < a + b < 2
=> l a + b l < 2
yup I am pretty much stuck here..pleasee help(i can't say l a + b l < l 1 + ab l because they are both<2..