## Non-calculator proof that ππ−π<1003\pi^\pi -\pi \lt \frac{100}{3}

I am looking for a few non-computational, non-calculator proof of the following inequality: ππ−π<1003 I can’t really seem to come up with a proof because of that killer ππ term. Answer The inequality xx−x<100/3 is true precisely when 0<x<3.14175798627357…, so intuitively a solution to this problem must in some fashion make use of the fact … Read more