Tell me, /sci/.

>>8598621
Everything
But it can't be defined as a function really

>>8598621
Its equal to the fiber defined by the inverse of pi(x) = 1^x at 1, which is isomorphic to the complex plain.

>>8598834
It is the complex plane, its that simple really

>>8598621
against god

>>8598621
Why is it not one? 1^1 =1

>>8598906
[math]1^x=1 ~~ \forall x \in \mathbb{R}[/math]

>>8598906
>>8599036
Same problem as 0/0.

For all a, 0*a=0.

J
And just like log_1(a) definitely has no solutions for a=/=1, a/0 has no solutions for a=/=0.

>>8599050
I'd say it's more of an "infinite solutions" type problem instead of a "no solutions" type, since there's an infinite amount of values that make this true. Also, I made a mistake in my post, I should've said [math]\forall x \in \mathbb{C}[/math].

Consider the change of base rule:
[eqn]
\log_a x = \frac{\log_b x}{\log_b a}
\Rightarrow
\log_1 1 = \frac{\ln 1}{\ln 1} = \frac{0}{0}
[eqn]

>>8598621
An exponent

>>8599250
Trying again:
Consider the change of base rule:
[eqn]
\log_a x = \frac{\log_b x}{\log_b a}
\Rightarrow
\log_1 1 = \frac{\ln 1}{\ln 1} = \frac{0}{0}
[/eqn]

>>8598621
1

zero

one to the zero power is one.

>>8598621
a^x = b, where a and b are positive, real numbers.
(e^ln(a))^x = b, e^x*ln(a) = b, x*ln(a) = ln(b)
ln(b)/ln(a) = x.
1^x = 1, (e^ln(1))^x = 1, e^x*0 = 1, x*0 = 0
x*0 = 0.