I'm working on a proof and I'm stuck at what seems to me a severe case of mathematician's block (which is sort of like writer's block). I need to prove that when you take a number greater than 1 and raise it to any power the result is going to be larger than the original number. In other words:
If and is a natural number, then .
Right right, greater than or equal to. With the natural numbers, there will be no though (beneath 1), because they start at 1 and count upwards by integers. A condition on the proof was that the exponent belong to the natural numbers. Therefore, by consequence, will always hold true since . Otherwise the conditions of the proof are violated and it's... what's that called... vacuously true I think.