Let be provided with

*
Note: To execute this problem, i think we must assume the visibility of an irrational number. We will certainly prove the visibility of together a number (the
*
) in I.3.12, practice #12.

Proof. because the rationals are dense in the reals I.3.12, practice #6, we know that for with

*
0" title="Rendered through QuickLaTeX.com" height="11" width="63" style="vertical-align: 0px;"/>, we understand there exists an essence
*
such that

*
w \implies s > \fracwn + r \>" title="Rendered through QuickLaTeX.com"/>

Also, due to the fact that

*
0" title="Rendered through QuickLaTeX.com" height="14" width="57" style="vertical-align: -3px;"/>, we have
*
0" title="Rendered by QuickLaTeX.com" height="16" width="39" style="vertical-align: -5px;"/>; thus,
*
irrational and hence
*
irrational.Thus, letting
*
, we have actually
*