So apparently it's not known if [math]\pi^{\pi^{\pi^\pi}}[/math] is an irrational number.
ITT: We find out.
(-1) = -1
(-1)(-1) = 1
(-1)(-1)(-1) = -1
>>8074729
Is that suposed to go on forever or is it just pi^pi^pi^pi?
>>8074744
OP here, it's just 4.
>>8074729
Why should we care whether a number is irrational or not?
It's not. Here's a proof by contraction: Suppose it is rational, let pi^pi^pi^pi = a/b, where a and b are """real""". Then we have (a/b)^(a/b) must be rational, which is a contraction as proved by Barnett in his 2013 seminal paper on exact ∞-groupoids in noncommutative cohomolgy Frobenioids in the framework of synthetic homotopical Grothendieck étale contravariants.
>>8074753
You don't need to care about it. It's a question for those who do care. If you don't care, don't enter the thread.
>>8074747
but what about [math]\pi^{\pi^{\pi^{\pi^{\pi^{\pi^{\pi^{\pi^{\pi^{\pi^{\pi^{\pi^{\pi^{\pi^{\pi^{\pi^{\pi^{\pi^{\pi^{\pi^{\pi^{\pi^{\pi^\pi}}}}}}}}}}}}}}}}}}}}}}[/math]?
>>8074772
Well, it's just one of the easiest examples of the bigger problem;
We don't know if there exists a power tower of [math]\pi[/math] and [math]e[/math] that is an integer.
>>8074763
But why do you care?
>>8074781
>[math]\pi[/math] and [math]e[/math]
*or
SOLUTION COMING
>>8074813
I was wrong
>>8074815
>>8074729
WOW IT'S FUCKING NOTHING
>>8074834
Only way it could be better is if it had a reddit tab open
>>8074744
if it went forever then it would be equal to +oo
There must be a bijection between the rational (positive) numbers and the subset of the irrational numbers that , when pi is raised to that irrational number equal a rational number.
therefore their cardinality is the same.
and so it is almost certain that pi^a is irrational if a is irrational.
>>8074891
almost certain aint good enough bruh, uncountable infinities are big
is pi^pi irrational? Then what's to stop any order of pi to be irrational?
>>8074729
OP, we don't even know if Pi times e is algebraic. We have a loooong way to go.
>>8075361
An irrational number to an irrational power isn't necessarily irrational.
>>8075376
√(-1)2 for example
>>8076914
Give an example within the reals
>>8076949
A = 2^(sqrt(2))
B = sqrt(2)
Both irrational.
A^B = 4
>>8074729
No, we don't
I wonder if theres a neat proof for pi^pi being transcendental, like e^pi being transcendental as
e^pi=(e^i*pi)^-1=(-1)^-i which is transcendental by gelfond schneider theorem
>>8074834
Once I saw /lgbt/, I thought the next tab was gonna be gay porn.
