Infinity * Zero = Any Number ARGUE HERE

[Reach]

If I made you immortal and told you to take an undecayable calculator and hit 1 then *1 for all eternity, you would never see another number besides one.

True. Hitting 1 forever doesn't equate to infinity though.

The reason why it's undefined in simple terms is because you don't know what infinity is. You're making a fallacious assumption when thinking 1^infinity means 1 times itself infinite times.

Infinity doesn't imply a number, what if infinity is a function? That's where the problem arises. Remember, infinity has no value, it just means to exist without bounds (existing everywhere at any given point in time). You can represent this unboundedness by any number of functions.


I suppose if you let x go to zero, lim hx^kx = (1+x)^(1/x) , then is that one?

No, no it's not. It's 1^infinity, but the answer is e. lny=(1/x)ln(1+x) , lny=ln(1+x)/x , dy/dx (H) = 1/1+x , let x go to 0, ln y= 1, y = e^1 = e

Contradiction! 1^infinity therefore does not have to equal 1...it can have any number of answers actually.

Hence the answer is undefined.