- #1
tomwilliam2
- 117
- 2
Homework Statement
I'm trying to show that if ##a \approx 1##, then
$$-1 \leq \frac{1-a}{a} \leq 1$$
I've started off trying a contradiction, i.e. suppose
$$ \frac{|1-a|}{a} > 1$$
either i)
$$\frac{1-a}{a} < -1$$
then multiply by a and add a to show
$$1 < 0$$
which is clearly false,
or ii)
$$1 < \frac{1-a}{a}$$
Which by the same reckoning leads me to
$$a < \frac{1}{2}$$
Which seems inconsistent with the original statement that ##a \approx 1##.
It's hardly a rock solid proof though, is it?
Is there a better way of doing this?
Thanks