Lectures on Constructive Mathematics. - Mathematics, Algorithms ...
Lectures on Constructive Mathematics. - Mathematics, Algorithms ...
Lectures on Constructive Mathematics. - Mathematics, Algorithms ...
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
For another n<strong>on</strong>c<strong>on</strong>structive proof, c<strong>on</strong>sider the statement:<br />
There exist irrati<strong>on</strong>al numbers a; b such that a b is rati<strong>on</strong>al.<br />
Either p p<br />
2<br />
2 is rati<strong>on</strong>al or it is irrati<strong>on</strong>al.<br />
In the …rst case, take a = b = p 2:<br />
In the sec<strong>on</strong>d case, take a = p p<br />
2<br />
2<br />
and b = p 2: