- #1

- 13

- 0

"Let

*E*be the set of all positive real numbers

*t*such that

*t*<

^{n}*x*."

Later on the proof goes:

"Assume

*y*>

^{n}*x*. Put

*k*=

*y*/

^{n}-x*ny*. Then 0 <

^{n-1}*k*<

*y*. If

*t*≥

*y - k*, we conclude that

*y*.

^{n}-t^{n}≤ y^{n}-(y-k)^{n}< kny^{n-1}= y^{n}-xThus

*t*, and

^{n}>x*t*is not a member of

*E*. It follows that

*y - k*is an upper bound of

*E*."

Why does it follow? Is it because the possibility that

*t = y - k*combined with the fact that

*t*mean that

^{n}>x*y-k*always has to be an upper bound of

*E*? Or is there some other reasoning?

Thanks in advance.