Re: how to prove this inequality

On Sat, 3 Sep 2005, Proginoskes wrote:

> William Elliot wrote:
> > On Sat, 3 Sep 2005, woodland wrote:
> >
> > > if a,b belong to R (set of real numbers), and
> > > a-c < b for any c >0 prove that a <= b
> > >
> > As c > 0, 0 < = -c
>
> WHAT!?!?!?

Whoops! As c > 0, -c <= 0.
To read the problem correctly
for all c > 0, a - c < b ==> a <= b

Assume premise. If not a <= b, then
b < a; 0 < a - b; let c = a - b
a - c = a - (a - b) = a + b - a = b
0 < c & not a - c < b, contradicts premise

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