- #1

- 13

- 0

## Main Question or Discussion Point

Firstly, the set E is defined:

"Let

Later on the proof goes:

"Assume

Thus

Why does it follow? Is it because the possibility that

Thanks in advance.

"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.